Normality and countable paracompactness of products with σ-spaces having special nets

On a class of σ-space with special nets

“…Firstly, to make it easier to read, we recall some definitions introduced in [2]. Let X be a space, A a family of subsets of X and U a subset of X.…”

“…In [2], the concept of strong σ -spaces is also introduced. A space X is called a strong σ -space if X has a sequence F n n∈ω of σ -locally finite closed covers such that,for every closed subset S of X, we have that n∈ω St (S, F n ) = S.…”

“…In the following, we use the same symbols as those in [2]. We denote by τ d the topology of a pseudometric space (X, d) and we use the symbols B d (x, r) and B d (x, r) to denote open and closed d-balls, respectively.…”

“…In a similar way, Junnila and Yajima in [2] defined the regular nets, and then they introduced a well-behaved class: P -netted spaces, where P denotes "PF" (point-finite), "LF" (locally finite), "CP" (closure preserving) or "HCP" (hereditarily closure-preserving).…”