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A space $X$ is called $CCS$-normal space if there exist a normal space $Y$ and a bijection $f: Xmapsto Y$ such that $flvert_C:Cmapsto f(C)$ is homeomorphism for any cellular-compact subset $C$ of $X$. We discuss about the relations between $C$-normal, $CC$-normal, $Ps$-normal spaces with $CCS$-normal.
A space $X$ is called $Ps$-normal($Ps$-Tychonoff) space if there exists a normal(Tychonoff) space $Y$ and a bijection $f: Xmapsto Y$ such that $flvert_K:Kmapsto f(K)$ is homeomorphism for any pseudocompact subset $K$ of $X$. We establish a few relati
We examine locally compact normal spaces in models of form PFA(S)[S], in particular characterizing paracompact, countably tight ones as those which include no perfect pre-image of omega_1 and in which all separable closed subspaces are Lindelof.
We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of omega_1 is hereditarily paracompact.
A theorem by Norman L. Noble from 1970 asserts that every product of completely regular, locally pseudo-compact k_R-spaces is a k_R-space. As a consequence, all direct products of locally compact Hausdorff spaces are k_R-spaces. We provide a streamlined proof for this fact.
W. Hurewicz proved that analytic Menger sets of reals are $sigma$-compact and that co-analytic completely Baire sets of reals are completely metrizable. It is natural to try to generalize these theorems to projective sets. This has previously been ac