On the Closure-Preserving Sum Theorem

Paracompactness with respect to an ideal

“…A subset A of a topological space (X, τ) is said to be a generalized F σ −subset [13] if for each open subset U of X containing A, there exists an F σ −subset B of X which is contained in U and contains A. A space X is said to be totally normal [12] if it is normal and every open subset G of X is expressible as a union of a locally finite (in G) family of open F σ −subset of X. A space X is said to be perfectly normal [6] if it is normal and in which each open set is an F σ −set.…”