On Structure of H-Spaces

Abstract

A pair (X,A) of a topological space X and a topological ring A is called an H-space, if for each closed subset F of X and x ∉ F, there exists f ∈ C_A(X) such that f(x) ≠ o_A and F ⊆ Z(f) and a topological space X is called a V-space, [4], if for points a, b, c, and d of X, where a ≠ b, there exists a continuous functions f of X into itself such that f(a) = c and f(b) = d. In this paper we investigate some properties of H-spaces. In addition to , we show that every H-space is not a V-space.

Key words and phrases. H-space, zero-dimensional, completely regular, topological ring.

2000 Mathematics Subject Classification. 49QJ20, 49J45, 49M25, 76D33