<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">This article is the continuation of [31]. We define the set of <italic>Lp</italic> integrable functions - the set of all partial functions whose absolute value raised to the <italic>p</italic>-th power is integrable. We show that <italic>Lp</italic> integrable functions form the <italic>Lp</italic> space. We also prove Minkowski's inequality, Hölder's inequality and that <italic>Lp</italic> space is Banach space ([15], [27]).</abstract>

Graduate School of Science and Technology, Shinshu University, Nagano, Japan

Gifu National College of Technology, Japan

On <italic>Lp</italic> Space Formed by Real-Valued Partial Functions

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">We prove that basic arithmetic operations preserve continuity of functions.</abstract>

On the Continuity of Some Functions

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

The Geometric Interior in Real Linear Spaces

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">In this article we give definitions of open functions and continuous functions formulated in terms of "balls" of given topological spaces.</abstract>

Miscellaneous Facts about Open Functions and Continuous Functions

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On L^p Space Formed by Real-Valued Partial Functions

On the Continuity of Some Functions

The Geometric Interior in Real Linear Spaces

Miscellaneous Facts about Open Functions and Continuous Functions

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On Lp Space Formed by Real-Valued Partial Functions

On the Continuity of Some Functions

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Miscellaneous Facts about Open Functions and Continuous Functions

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On L^p Space Formed by Real-Valued Partial Functions