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Special Issue: 25 years of the Mizar Mathematical Library

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Journal Details
Format
Journal
eISSN
1898-9934
ISSN
1426-2630
First Published
09 Jun 2008
Publication timeframe
4 times per year
Languages
English

Search

Volume 18 (2010): Issue 3 (January 2010)

Journal Details
Format
Journal
eISSN
1898-9934
ISSN
1426-2630
First Published
09 Jun 2008
Publication timeframe
4 times per year
Languages
English

Search

0 Articles
Open Access

On Lp Space Formed by Real-Valued Partial Functions

Yasushige Watase,
Yasushige Watase,
Noboru Endou and
Noboru Endou and
Yasunari Shidama
Yasunari Shidama
Published Online: 05 Jan 2011
Page range: 159 - 169

Abstract

On <italic>L<sup>p</sup></italic> Space Formed by Real-Valued Partial Functions

This article is the continuation of [31]. We define the set of Lp integrable functions - the set of all partial functions whose absolute value raised to the p-th power is integrable. We show that Lp integrable functions form the Lp space. We also prove Minkowski's inequality, Hölder's inequality and that Lp space is Banach space ([15], [27]).

Open Access

Miscellaneous Facts about Open Functions and Continuous Functions

Artur Korniłowicz
Artur Korniłowicz
Published Online: 05 Jan 2011
Page range: 171 - 174

Abstract

Miscellaneous Facts about Open Functions and Continuous Functions

In this article we give definitions of open functions and continuous functions formulated in terms of "balls" of given topological spaces.

Open Access

On the Continuity of Some Functions

Artur Korniłowicz
Artur Korniłowicz
Published Online: 05 Jan 2011
Page range: 175 - 183

Abstract

On the Continuity of Some Functions

We prove that basic arithmetic operations preserve continuity of functions.

Open Access

The Geometric Interior in Real Linear Spaces

Karol Pąk
Karol Pąk
Published Online: 05 Jan 2011
Page range: 185 - 188

Abstract

The Geometric Interior in Real Linear Spaces

We introduce the notions of the geometric interior and the centre of mass for subsets of real linear spaces. We prove a number of theorems concerning these notions which are used in the theory of abstract simplicial complexes.

0 Articles
Open Access

On Lp Space Formed by Real-Valued Partial Functions

Yasushige Watase,
Yasushige Watase,
Noboru Endou and
Noboru Endou and
Yasunari Shidama
Yasunari Shidama
Published Online: 05 Jan 2011
Page range: 159 - 169

Abstract

On <italic>L<sup>p</sup></italic> Space Formed by Real-Valued Partial Functions

This article is the continuation of [31]. We define the set of Lp integrable functions - the set of all partial functions whose absolute value raised to the p-th power is integrable. We show that Lp integrable functions form the Lp space. We also prove Minkowski's inequality, Hölder's inequality and that Lp space is Banach space ([15], [27]).

Open Access

Miscellaneous Facts about Open Functions and Continuous Functions

Artur Korniłowicz
Artur Korniłowicz
Published Online: 05 Jan 2011
Page range: 171 - 174

Abstract

Miscellaneous Facts about Open Functions and Continuous Functions

In this article we give definitions of open functions and continuous functions formulated in terms of "balls" of given topological spaces.

Open Access

On the Continuity of Some Functions

Artur Korniłowicz
Artur Korniłowicz
Published Online: 05 Jan 2011
Page range: 175 - 183

Abstract

On the Continuity of Some Functions

We prove that basic arithmetic operations preserve continuity of functions.

Open Access

The Geometric Interior in Real Linear Spaces

Karol Pąk
Karol Pąk
Published Online: 05 Jan 2011
Page range: 185 - 188

Abstract

The Geometric Interior in Real Linear Spaces

We introduce the notions of the geometric interior and the centre of mass for subsets of real linear spaces. We prove a number of theorems concerning these notions which are used in the theory of abstract simplicial complexes.