PM-normality and the insertion of a continuous function

Some embeddings related to C*-embeddings

“…can show that X is Oz by using the fact that every point of X is a zero set and the fact that FT is Oz. This establishes that regular closed sets are C*-embedded since Oz-spaces are metanormal [15] and [19].…”

“…Lane [15] and Shchepin [19] have shown that every Oz-space is MN and Noble [18] has shown that the product of real lines is Oz. EXAMPLE 4.9.…”

“…THEOREM 8.1. Every Oz-space is MN [15]. An MN F'-space is an F-space [9] have constructed an F'-space that is not an /"-space.…”

Inserting L‐fuzzy Real‐valued Functions

“…Both the KatEtov-Tong and Tietze-Urysohn theorems hold true for normal L-fuzzy topological spaces, as proved in [17] by utilizing Kat6tov's method of proof (see also [18] for further generalization a la BLAIR [3] and LANE [21]). We notice that the techniques of BONAN and SCOTT work in the fuzzy situation as well.…”

Lebesgue sets and insertion of a continuous function

“…The results of Blatter and Seever in [3 and 4] require that the classes U(X) and L(X) can be characterized as cn(A) and cñ(B), respectively, for some sublattices A and B of the power set of X and that Ac B& (= intersection of sequences in B) and B c At (= union of sequences in A). The necessary (as proved by Powderly [13]) and sufficient condition of [7] places restrictions on the function f -g. These limitations are avoided in Theorem 2.…”