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2017•Hacettepe Journal of Mathematics and StatisticsOpen access

FUNCTIONAL EQUIVALENCE OF TOPOLOGICAL SPACES AND TOPOLOGICAL MODULES

Mitrofan M. Choban

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Abstract

Let R be a topological ring and E, F be unitary topological R-modules.Denote by Cp(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 lp(E, F )-equivalent if the topological R-modules Cp(X, E) and Cp(Y, F ) are topological isomorphic.Some conditions under which the topological property P is preserved by the lp(E, F )-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.

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Let R be a topological ring and E, F be unitary topological R-modules.Denote by Cp(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 lp(E, F )-equivalent if the topological R-modules Cp(X, E) and Cp(Y, F ) are topological isomorphic.Some conditions under which the topological property P is preserved by the lp(E, F )-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.

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Available abstract

Let R be a topological ring and E, F be unitary topological R-modules.Denote by Cp(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 lp(E, F )-equivalent if the topological R-modules Cp(X, E) and Cp(Y, F ) are topological isomorphic.Some conditions under which the topological property P is preserved by the lp(E, F )-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.

Key concepts: Mathematics, Topological space, Topology (electrical circuits), Homeomorphism (graph theory), Topological algebra, Topological dynamics, Equivalence (formal languages), Topological vector space

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