Zeszyty czasopisma

Tom 80 (2021): Zeszyt 3 (December 2021)

Tom 79 (2021): Zeszyt 2 (December 2021)

Tom 78 (2021): Zeszyt 1 (October 2021)

Tom 77 (2020): Zeszyt 1 (December 2020)

Tom 76 (2020): Zeszyt 1 (December 2020)
Real Functions, Dynamical Systems and their Applications

Tom 75 (2020): Zeszyt 1 (April 2020)
Applied Mathematics'19

Tom 74 (2019): Zeszyt 1 (December 2019)
Real Functons, Ideals, Measurable Functions, Functional Equations

Tom 73 (2019): Zeszyt 1 (August 2019)
Number Theory, Algebra and Cryptology '18

Tom 72 (2018): Zeszyt 1 (December 2018)

Tom 71 (2018): Zeszyt 1 (December 2018)

Tom 70 (2017): Zeszyt 1 (September 2017)

Tom 69 (2017): Zeszyt 1 (June 2017)

Tom 68 (2017): Zeszyt 1 (March 2017)
Special Zeszyt: Real Functions ’16, Real Functions, Density Topologies, Porosity

Tom 67 (2016): Zeszyt 1 (September 2016)

Tom 66 (2016): Zeszyt 1 (June 2016)
Zeszyt title: Applied Mathematics ’16

Tom 65 (2016): Zeszyt 1 (March 2016)
Real Functions '15 — Measure Theory, Real Functions, General Topology. Editors: J. Borsík, 2016.

Tom 64 (2015): Zeszyt 1 (September 2015)
Number Theory and Cryptology ’15

Tom 62 (2015): Zeszyt 1 (March 2015)
Special Zeszyt Title: Real Functions ’14

Tom 61 (2014): Zeszyt 1 (December 2014)
Special Zeszyt Title: Applied Mathematics ‘14

Tom 60 (2014): Zeszyt 1 (September 2014)
Special Zeszyt Title: Cryptology ’14

Tom 59 (2014): Zeszyt 1 (June 2014)
Special Zeszyt Title: Number Theory ‘14

Tom 58 (2014): Zeszyt 1 (March 2014)
Real Functions ‘13 Real Functions, Topology, Real and Functional Analysis, Locally Convex Spaces

Tom 57 (2013): Zeszyt 1 (December 2013)
Cryptology

Tom 56 (2013): Zeszyt 1 (November 2013)
Number Theory

Tom 55 (2013): Zeszyt 1 (August 2013)

Tom 54 (2013): Zeszyt 1 (April 2013)
Differential and Difference Equations and Applications ‘2012

Tom 53 (2012): Zeszyt 1 (December 2012)
TATRACRYPT ‘12

Tom 52 (2012): Zeszyt 1 (August 2012)

Tom 51 (2012): Zeszyt 1 (April 2012)
PROBASTAT ‘11

Tom 50 (2011): Zeszyt 1 (December 2011)
Applied Mathematics and Informatics

Tom 49 (2011): Zeszyt 1 (August 2011)
Real Functions ‘10

Tom 48 (2011): Zeszyt 1 (April 2011)
Differential and Difference Equations and Applications 2010

Tom 47 (2010): Zeszyt 1 (December 2010)
CCEC ‘09

Tom 46 (2010): Zeszyt 1 (August 2010)
Real Functions ‘09

Tom 45 (2010): Zeszyt 1 (April 2010)
NILCRYPT ‘10

Tom 44 (2009): Zeszyt 1 (December 2009)
Real Function ’08 Functional Equation, Measures, Integration and Harmonic Analysis

Tom 43 (2009): Zeszyt 1 (August 2009)
Differential and Difference Equations and Applications 2008

Tom 42 (2009): Zeszyt 1 (April 2009)
Real Function ‘07

Informacje o czasopiśmie
Format
Czasopismo
eISSN
1338-9750
ISSN
1210-3195
Pierwsze wydanie
12 Nov 2012
Częstotliwość wydawania
3 razy w roku
Języki
Angielski

Wyszukiwanie

Tom 46 (2010): Zeszyt 1 (August 2010)
Real Functions ‘09

Informacje o czasopiśmie
Format
Czasopismo
eISSN
1338-9750
ISSN
1210-3195
Pierwsze wydanie
12 Nov 2012
Częstotliwość wydawania
3 razy w roku
Języki
Angielski

Wyszukiwanie

14 Artykułów
Otwarty dostęp

A characteristic of i-connected spaces

Data publikacji: 13 Nov 2012
Zakres stron: 1 - 103

Abstrakt

Abstract

A theorem characterizing -connected spaces, which are completely Hausdorff, separable, locally and arcwise connected, is presented.

Słowa kluczowe

  • i-connected space
  • completely Hausdorff space
  • locally connected arcwise connected space
Otwarty dostęp

On homeomorphisms of density type topologies generated by functions

Data publikacji: 13 Nov 2012
Zakres stron: 7 - 13

Abstrakt

Abstract

The paper is concerned with homeomorphisms on topological spaces (ℝ, Tƒ), where Tƒ is a generalization of the density topology generated by a function ƒ. It is shown that the density topology is not homeomorphic with any other topology Tƒ and that, under some assumptions, homeomorphic ƒ-density topologies have to be comparable.

Słowa kluczowe

  • density point
  • density topology
  • homeomorphism.
Otwarty dostęp

Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions

Data publikacji: 13 Nov 2012
Zakres stron: 15 - 27

Abstrakt

Abstract

We present new sufficient conditions for the existence of a continuous utility function for an arbitrary binary relation on a topological space. Such conditions are basically obtained by using both the concept of a weakly continuous binary relation on a topological space and the concept of a network weight. We are concerning with suitable topological notions which generalize the concept of compactness and do not imply second countability or local compactness.

Słowa kluczowe

  • hereditarily Lindel¨of space
  • weakly continuous binary relation
  • countable network weight
  • hemicompactness
  • submetrizability.
Otwarty dostęp

Some convergence theorems for bk-integral in locally convex spaces

Data publikacji: 13 Nov 2012
Zakres stron: 29 - 40

Abstrakt

Abstract

In this paper, we present some convergence theorems for Bkintegral of functions taking values in a locally convex topological vector space. These theorems are involved with the notion of equi-Bk-integrability.

Słowa kluczowe

  • Bk-integral
  • locally convex topological vector space
  • convergence theorems
  • equi- Bk-integrability.
Otwarty dostęp

On smítal property

Data publikacji: 13 Nov 2012
Zakres stron: 47 - 54

Abstrakt

Abstract

In this paper, we define and study the property called Sm´ıtal property for the pair (M, I), where M denotes a σ-algebra of subsets of real line and I M is a σ-ideal. It is a generalization of Sm´ıtal lemma. We give some examples of pairs (M, I) having Sm´ıtal property and pairs which do not have this property.

Słowa kluczowe

  • Sm´ıtal lemma
  • Sm´ıtal property
  • Borel measure
  • Lebesgue-Stieltjes measure.
Otwarty dostęp

Strict density topology of the plane. category case

Data publikacji: 13 Nov 2012
Zakres stron: 55 - 64

Abstrakt

Abstract

We study the properties of category density topology of the plane generated by a restricted convergence in the category of double sequences of characteristic functions and more interesting topology generated by a strict convergence in the category of the same sequences, which is a natural modification of a previous one. Similar problems for measure density were considered in [M. Filipczak, W. Wilczy´nski: Strict density topology on the plane. Measure case (in preparation)].

Słowa kluczowe

  • category density of the plane
  • convergence in the restricted sense
  • separation axioms.
Otwarty dostęp

Application of Hurewicz theorem to classification of Π11 -complete sets

Data publikacji: 13 Nov 2012
Zakres stron: 65 - 69

Abstrakt

Abstract

We present a simple proof of a dichotomy theorem by Kechris- -Louveau-Woodin [Kechris, A. S., Louveau, A.: Descriptive set theory and thestructure of sets of uniqueness, London Math. Soc. Lecture Note Ser. 128 (1987), 104-138] telling that every Π11σ-ideal of compact subsets of a Polish space is either Gδ or else Π11 -complete.

Słowa kluczowe

  • analytic set
  • coanalytic set
  • Π<sup>1</sup><sub>1</sub> -complete set
  • hyperspace
  • σ-ideal of compact sets
  • Hurewicz theorem.
Otwarty dostęp

Wqn spaces and related notions

Data publikacji: 13 Nov 2012
Zakres stron: 71 - 77

Abstrakt

Słowa kluczowe

  • Lower and upper semicontinuous functions
  • properties wQN<sub>*</sub>
  • wQN<sup>*</sup>
  • SSP<sub>* </sub>and SSP<sup>*</sup>.

  • Abstract We discuss modifications of wQN and SSP properties for semicontinuous functions with values in some special sets of reals and we give the relations among these notions. We present direct proofs of wQN* → wQN ∗ and SSP∗ → SSP∗.
Otwarty dostęp

Nonmeasurable sets with regular sections

Data publikacji: 13 Nov 2012
Zakres stron: 79 - 83

Abstrakt

Słowa kluczowe

  • Sierpi´nski set
  • nonmeasurable sets on the plane
  • sections of the plane set
Otwarty dostęp

Some remarks on ρ-upper continuous functions

Data publikacji: 13 Nov 2012
Zakres stron: 85 - 89

Abstrakt

Słowa kluczowe

  • density of a set at a point
  • ρ-upper continuous functions
  • approximately continuous functions
  • Baire 1 functions
  • Denjoy property.
Otwarty dostęp

On some characterizations of Baire class one functions and Baire class one like functions

Data publikacji: 13 Nov 2012
Zakres stron: 91 - 106

Abstrakt

Abstract

The basis of our considerations is a characterization of Baire class one functions presented by [Pen-Yee Lee - Wee-Kee Tang - Doingsheng Zhao: An equivalent definition of functions of the first Baire class, in: Proc. Amer. Math. Soc., Vol. 129, 2000, pp. 2273-2275]. In the first part of this paper, we will prove an analogous characterization for functions belonging to the class . In the last part, we will consider various classes of functions connected with the characterization mentioned above, which permits to give a new characterization of Baire class one functions.

Słowa kluczowe

  • Baire one function. B<sub>1</sub>**-function
  • uniformly continuous function
  • lower semicontinuous function
  • weakly lower semicontinuous function
  • upper semicontinuous function.
Otwarty dostęp

The diestel-faires theorem on series

Data publikacji: 13 Nov 2012
Zakres stron: 107 - 110

Abstrakt

Słowa kluczowe

  • subseries convergence
  • weak*.
Otwarty dostęp

A Helly theorem in metric spaces and majored operations

Data publikacji: 13 Nov 2012
Zakres stron: 111 - 123

Abstrakt

Słowa kluczowe

  • metric space
  • vector space
  • vector function
  • bounded variation
  • majored operator. Supported by grant agency Vega
  • N. 2/0212/10.
Otwarty dostęp

On the Lukasiewicz probability theory on IF-sets

Data publikacji: 13 Nov 2012
Zakres stron: 125 - 146

Abstrakt

Słowa kluczowe

  • probability
  • IF-set
  • limit theorems.
14 Artykułów
Otwarty dostęp

A characteristic of i-connected spaces

Data publikacji: 13 Nov 2012
Zakres stron: 1 - 103

Abstrakt

Abstract

A theorem characterizing -connected spaces, which are completely Hausdorff, separable, locally and arcwise connected, is presented.

Słowa kluczowe

  • i-connected space
  • completely Hausdorff space
  • locally connected arcwise connected space
Otwarty dostęp

On homeomorphisms of density type topologies generated by functions

Data publikacji: 13 Nov 2012
Zakres stron: 7 - 13

Abstrakt

Abstract

The paper is concerned with homeomorphisms on topological spaces (ℝ, Tƒ), where Tƒ is a generalization of the density topology generated by a function ƒ. It is shown that the density topology is not homeomorphic with any other topology Tƒ and that, under some assumptions, homeomorphic ƒ-density topologies have to be comparable.

Słowa kluczowe

  • density point
  • density topology
  • homeomorphism.
Otwarty dostęp

Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions

Data publikacji: 13 Nov 2012
Zakres stron: 15 - 27

Abstrakt

Abstract

We present new sufficient conditions for the existence of a continuous utility function for an arbitrary binary relation on a topological space. Such conditions are basically obtained by using both the concept of a weakly continuous binary relation on a topological space and the concept of a network weight. We are concerning with suitable topological notions which generalize the concept of compactness and do not imply second countability or local compactness.

Słowa kluczowe

  • hereditarily Lindel¨of space
  • weakly continuous binary relation
  • countable network weight
  • hemicompactness
  • submetrizability.
Otwarty dostęp

Some convergence theorems for bk-integral in locally convex spaces

Data publikacji: 13 Nov 2012
Zakres stron: 29 - 40

Abstrakt

Abstract

In this paper, we present some convergence theorems for Bkintegral of functions taking values in a locally convex topological vector space. These theorems are involved with the notion of equi-Bk-integrability.

Słowa kluczowe

  • Bk-integral
  • locally convex topological vector space
  • convergence theorems
  • equi- Bk-integrability.
Otwarty dostęp

On smítal property

Data publikacji: 13 Nov 2012
Zakres stron: 47 - 54

Abstrakt

Abstract

In this paper, we define and study the property called Sm´ıtal property for the pair (M, I), where M denotes a σ-algebra of subsets of real line and I M is a σ-ideal. It is a generalization of Sm´ıtal lemma. We give some examples of pairs (M, I) having Sm´ıtal property and pairs which do not have this property.

Słowa kluczowe

  • Sm´ıtal lemma
  • Sm´ıtal property
  • Borel measure
  • Lebesgue-Stieltjes measure.
Otwarty dostęp

Strict density topology of the plane. category case

Data publikacji: 13 Nov 2012
Zakres stron: 55 - 64

Abstrakt

Abstract

We study the properties of category density topology of the plane generated by a restricted convergence in the category of double sequences of characteristic functions and more interesting topology generated by a strict convergence in the category of the same sequences, which is a natural modification of a previous one. Similar problems for measure density were considered in [M. Filipczak, W. Wilczy´nski: Strict density topology on the plane. Measure case (in preparation)].

Słowa kluczowe

  • category density of the plane
  • convergence in the restricted sense
  • separation axioms.
Otwarty dostęp

Application of Hurewicz theorem to classification of Π11 -complete sets

Data publikacji: 13 Nov 2012
Zakres stron: 65 - 69

Abstrakt

Abstract

We present a simple proof of a dichotomy theorem by Kechris- -Louveau-Woodin [Kechris, A. S., Louveau, A.: Descriptive set theory and thestructure of sets of uniqueness, London Math. Soc. Lecture Note Ser. 128 (1987), 104-138] telling that every Π11σ-ideal of compact subsets of a Polish space is either Gδ or else Π11 -complete.

Słowa kluczowe

  • analytic set
  • coanalytic set
  • Π<sup>1</sup><sub>1</sub> -complete set
  • hyperspace
  • σ-ideal of compact sets
  • Hurewicz theorem.
Otwarty dostęp

Wqn spaces and related notions

Data publikacji: 13 Nov 2012
Zakres stron: 71 - 77

Abstrakt

Słowa kluczowe

  • Lower and upper semicontinuous functions
  • properties wQN<sub>*</sub>
  • wQN<sup>*</sup>
  • SSP<sub>* </sub>and SSP<sup>*</sup>.

  • Abstract We discuss modifications of wQN and SSP properties for semicontinuous functions with values in some special sets of reals and we give the relations among these notions. We present direct proofs of wQN* → wQN ∗ and SSP∗ → SSP∗.
Otwarty dostęp

Nonmeasurable sets with regular sections

Data publikacji: 13 Nov 2012
Zakres stron: 79 - 83

Abstrakt

Słowa kluczowe

  • Sierpi´nski set
  • nonmeasurable sets on the plane
  • sections of the plane set
Otwarty dostęp

Some remarks on ρ-upper continuous functions

Data publikacji: 13 Nov 2012
Zakres stron: 85 - 89

Abstrakt

Słowa kluczowe

  • density of a set at a point
  • ρ-upper continuous functions
  • approximately continuous functions
  • Baire 1 functions
  • Denjoy property.
Otwarty dostęp

On some characterizations of Baire class one functions and Baire class one like functions

Data publikacji: 13 Nov 2012
Zakres stron: 91 - 106

Abstrakt

Abstract

The basis of our considerations is a characterization of Baire class one functions presented by [Pen-Yee Lee - Wee-Kee Tang - Doingsheng Zhao: An equivalent definition of functions of the first Baire class, in: Proc. Amer. Math. Soc., Vol. 129, 2000, pp. 2273-2275]. In the first part of this paper, we will prove an analogous characterization for functions belonging to the class . In the last part, we will consider various classes of functions connected with the characterization mentioned above, which permits to give a new characterization of Baire class one functions.

Słowa kluczowe

  • Baire one function. B<sub>1</sub>**-function
  • uniformly continuous function
  • lower semicontinuous function
  • weakly lower semicontinuous function
  • upper semicontinuous function.
Otwarty dostęp

The diestel-faires theorem on series

Data publikacji: 13 Nov 2012
Zakres stron: 107 - 110

Abstrakt

Słowa kluczowe

  • subseries convergence
  • weak*.
Otwarty dostęp

A Helly theorem in metric spaces and majored operations

Data publikacji: 13 Nov 2012
Zakres stron: 111 - 123

Abstrakt

Słowa kluczowe

  • metric space
  • vector space
  • vector function
  • bounded variation
  • majored operator. Supported by grant agency Vega
  • N. 2/0212/10.
Otwarty dostęp

On the Lukasiewicz probability theory on IF-sets

Data publikacji: 13 Nov 2012
Zakres stron: 125 - 146

Abstrakt

Słowa kluczowe

  • probability
  • IF-set
  • limit theorems.

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