http://hdl.handle.net/11320/3542 2026-06-01T20:19:31Z http://hdl.handle.net/11320/3570 Tytuł: On Lp Space Formed by Real-Valued Partial Functions Autorzy: Watase, Yasushige; Endou, Noboru; Shidama, Yasunari Abstrakt: 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]). 2010-01-01T00:00:00Z http://hdl.handle.net/11320/3572 Tytuł: On the Continuity of Some Functions Autorzy: Korniłowicz, Artur Abstrakt: We prove that basic arithmetic operations preserve continuity of functions. 2010-01-01T00:00:00Z http://hdl.handle.net/11320/3571 Tytuł: Miscellaneous Facts about Open Functions and Continuous Functions Autorzy: Korniłowicz, Artur Abstrakt: In this article we give definitions of open functions and continuous functions formulated in terms of "balls" of given topological spaces. 2010-01-01T00:00:00Z http://hdl.handle.net/11320/3573 Tytuł: The Geometric Interior in Real Linear Spaces Autorzy: Pąk, Karol Abstrakt: 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. 2010-01-01T00:00:00Z