Functional equivalence of topological spaces and topological modules

Year 2017, Volume: 46 Issue: 1, 77 - 90, 01.02.2017

Mitrofan M. Choban , Radu N. Dumbraveanu

Abstract

Let $R$ be a topological ring and $E$, $F$ be unitary topological $R$-modules. Denote by $C_p(X,E)$ the class of all continuous mappings of $X$ into $E$ in the topology of pointwise convergence. The spaces $X$ and $Y$ are called $l_p(E,F)$-equivalent if the topological $R$-modules $C_p(X,E)$ and $C_p(Y,F)$ are topological isomorphic. Some conditions under which the topological property $\mathcal{P}$ is preserved by the $l_p(E,F)$-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.

Keywords

Function space, topology of pointwise convergence, support, linear homeomorphism, perfect properties, open finite-to-one properties

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