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Detalles de la revista
Formato
Revista
eISSN
1338-9750
ISSN
1210-3195
Publicado por primera vez
12 Nov 2012
Periodo de publicación
3 veces al año
Idiomas
Inglés

Buscar

Volumen 46 (2010): Edición 1 (August 2010)
Real Functions ‘09

Detalles de la revista
Formato
Revista
eISSN
1338-9750
ISSN
1210-3195
Publicado por primera vez
12 Nov 2012
Periodo de publicación
3 veces al año
Idiomas
Inglés

Buscar

14 Artículos
Acceso abierto

A characteristic of i-connected spaces

Publicado en línea: 13 Nov 2012
Páginas: 1 - 103

Resumen

Abstract

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

Palabras clave

  • i-connected space
  • completely Hausdorff space
  • locally connected arcwise connected space
Acceso abierto

On homeomorphisms of density type topologies generated by functions

Publicado en línea: 13 Nov 2012
Páginas: 7 - 13

Resumen

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.

Palabras clave

  • density point
  • density topology
  • homeomorphism.
Acceso abierto

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

Publicado en línea: 13 Nov 2012
Páginas: 15 - 27

Resumen

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.

Palabras clave

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

Some convergence theorems for bk-integral in locally convex spaces

Publicado en línea: 13 Nov 2012
Páginas: 29 - 40

Resumen

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.

Palabras clave

  • Bk-integral
  • locally convex topological vector space
  • convergence theorems
  • equi- Bk-integrability.
Acceso abierto

On smítal property

Publicado en línea: 13 Nov 2012
Páginas: 47 - 54

Resumen

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.

Palabras clave

  • Sm´ıtal lemma
  • Sm´ıtal property
  • Borel measure
  • Lebesgue-Stieltjes measure.
Acceso abierto

Strict density topology of the plane. category case

Publicado en línea: 13 Nov 2012
Páginas: 55 - 64

Resumen

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)].

Palabras clave

  • category density of the plane
  • convergence in the restricted sense
  • separation axioms.
Acceso abierto

Application of Hurewicz theorem to classification of Π11 -complete sets

Publicado en línea: 13 Nov 2012
Páginas: 65 - 69

Resumen

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.

Palabras clave

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

Wqn spaces and related notions

Publicado en línea: 13 Nov 2012
Páginas: 71 - 77

Resumen

Palabras clave

  • 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∗.
Acceso abierto

Nonmeasurable sets with regular sections

Publicado en línea: 13 Nov 2012
Páginas: 79 - 83

Resumen

Palabras clave

  • Sierpi´nski set
  • nonmeasurable sets on the plane
  • sections of the plane set
Acceso abierto

Some remarks on ρ-upper continuous functions

Publicado en línea: 13 Nov 2012
Páginas: 85 - 89

Resumen

Palabras clave

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

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

Publicado en línea: 13 Nov 2012
Páginas: 91 - 106

Resumen

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.

Palabras clave

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

The diestel-faires theorem on series

Publicado en línea: 13 Nov 2012
Páginas: 107 - 110

Resumen

Palabras clave

  • subseries convergence
  • weak*.
Acceso abierto

A Helly theorem in metric spaces and majored operations

Publicado en línea: 13 Nov 2012
Páginas: 111 - 123

Resumen

Palabras clave

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

On the Lukasiewicz probability theory on IF-sets

Publicado en línea: 13 Nov 2012
Páginas: 125 - 146

Resumen

Palabras clave

  • probability
  • IF-set
  • limit theorems.
14 Artículos
Acceso abierto

A characteristic of i-connected spaces

Publicado en línea: 13 Nov 2012
Páginas: 1 - 103

Resumen

Abstract

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

Palabras clave

  • i-connected space
  • completely Hausdorff space
  • locally connected arcwise connected space
Acceso abierto

On homeomorphisms of density type topologies generated by functions

Publicado en línea: 13 Nov 2012
Páginas: 7 - 13

Resumen

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.

Palabras clave

  • density point
  • density topology
  • homeomorphism.
Acceso abierto

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

Publicado en línea: 13 Nov 2012
Páginas: 15 - 27

Resumen

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.

Palabras clave

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

Some convergence theorems for bk-integral in locally convex spaces

Publicado en línea: 13 Nov 2012
Páginas: 29 - 40

Resumen

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.

Palabras clave

  • Bk-integral
  • locally convex topological vector space
  • convergence theorems
  • equi- Bk-integrability.
Acceso abierto

On smítal property

Publicado en línea: 13 Nov 2012
Páginas: 47 - 54

Resumen

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.

Palabras clave

  • Sm´ıtal lemma
  • Sm´ıtal property
  • Borel measure
  • Lebesgue-Stieltjes measure.
Acceso abierto

Strict density topology of the plane. category case

Publicado en línea: 13 Nov 2012
Páginas: 55 - 64

Resumen

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)].

Palabras clave

  • category density of the plane
  • convergence in the restricted sense
  • separation axioms.
Acceso abierto

Application of Hurewicz theorem to classification of Π11 -complete sets

Publicado en línea: 13 Nov 2012
Páginas: 65 - 69

Resumen

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.

Palabras clave

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

Wqn spaces and related notions

Publicado en línea: 13 Nov 2012
Páginas: 71 - 77

Resumen

Palabras clave

  • 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∗.
Acceso abierto

Nonmeasurable sets with regular sections

Publicado en línea: 13 Nov 2012
Páginas: 79 - 83

Resumen

Palabras clave

  • Sierpi´nski set
  • nonmeasurable sets on the plane
  • sections of the plane set
Acceso abierto

Some remarks on ρ-upper continuous functions

Publicado en línea: 13 Nov 2012
Páginas: 85 - 89

Resumen

Palabras clave

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

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

Publicado en línea: 13 Nov 2012
Páginas: 91 - 106

Resumen

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.

Palabras clave

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

The diestel-faires theorem on series

Publicado en línea: 13 Nov 2012
Páginas: 107 - 110

Resumen

Palabras clave

  • subseries convergence
  • weak*.
Acceso abierto

A Helly theorem in metric spaces and majored operations

Publicado en línea: 13 Nov 2012
Páginas: 111 - 123

Resumen

Palabras clave

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

On the Lukasiewicz probability theory on IF-sets

Publicado en línea: 13 Nov 2012
Páginas: 125 - 146

Resumen

Palabras clave

  • probability
  • IF-set
  • limit theorems.

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