- Hacettepe Journal of Mathematics and Statistics
- Vol: 46 Issue: 1
- Functional equivalence of topological spaces and topological modules
Functional equivalence of topological spaces and topological modules
Authors : Mitrofan M. Choban, Radu N. Dumbraveanu
Pages : 77-90
View : 12 | Download : 4
Publication Date : 2017-02-01
Article Type : Research
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