Functional equivalence of topological spaces and topological modules

摘要

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 P is preserved by the l(p) (E, F)-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.