We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of every locally compact, perfectly normal space is paracompact.

A space X is submaximal if any dense subset of open. In this paper, we prove that every topological gyrogroup non-measurable cardinality strongly ?-discrete. Moreover, hereditarily paracompact.

We present a simpler proof of the known theorem that a fixed-point free homeomorphism on an n-dimensional paracompact space can be colored with n+ 3 colors.  1999 Elsevier Science B.V. All rights reserved.

We prove that, if there is a model of set-theory which contains no first countable, locally compact, scattered Dowker spaces, then there is an inner model which contains a measurable cardinal. A Hausdorff space is normal if, for every pair of disjoint closed sets C and D, there is a pair of disjoint open sets, U containing C and V containing D. A (normal) space is binormal if its product with t...

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

In this paper we define pairwise-$\alpha$-paracompact subsets as a generalisation of $\alpha$-paracompact in topological spaces and study their properties its relations with other bitopological spaces. Several theorems are obtained concerning sets. We introduced the definition $p$-paracompact bitoplogical

We prove that if there is a model of set-theory which contains no first countable, locally compact, scattered, countably paracompact space X, whose Tychonoff square is a Dowker space, then there is an inner model which contains a measurable cardinal.

We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel’skĭı and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in [ω] , and a version of an (ω, 1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a pos...