On Extending of Solutions of Functional Equations in a Single Variable

Karol Baron

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Non-continuous linear functionals on topological vector spaces.

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Alexandroff One Point Compactification

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In the article, I introduce the notions of the compactification of topological spaces and the Alexandroff one point compactification. Some properties of the locally compact spaces and one point compactification are proved.

On continuous solutions of a functional equation

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This paper discusses continuous solutions of the functional equation φ[f(x)] = g(x,φ(x)) in topological spaces.

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When is L(X) topologizable as a topological algebra?

W. Żelazko (2002)

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Let X be a locally convex space and L(X) be the algebra of all continuous endomorphisms of X. It is known (Esterle [2], [3]) that if L(X) is topologizable as a topological algebra, then the space X is subnormed. We show that in the case when X is sequentially complete this condition is also sufficient. In this case we also obtain some other conditions equivalent to the topologizability of L(X). We also exhibit a class of subnormed spaces X, called sub-Banach spaces, which are not necessarily...