On the 𝑯-space and the product of two 𝑯-spaces

Abstract

Considering the set of real numbers R, for each x ∈ A, B(x)={(x−ϵ,x+ϵ):ϵ>0}, and for each x∈ R\A, let B(x)={[x,x+ϵ):ϵ>0}, the unique topology generated by {B(x): x ∈ R} is denoted by τ(A) and ( R , τ(A) ) is called an H-space. In this paper, we give some results about these spaces and the product of two of them, including the separation axioms, wD property, various types of compactness and connectedness, and weaker properties of normality.