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.

In this note, we show that cite[Corollary 3.2]{sad} is not always true. In fact, we characterize essential left $phi$-contractibility of the group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group $G$, $L^{2}(G)$ is always essentially left $phi$-contractible. We discuss the essential left $phi$-contractibility of some Fou...

Ramı́rez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [A reflection theorem for i-weight , Topology Proc. 28 (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of ...

In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.

In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.

This paper pays a visit to famous contractible open 3-manifold $W^3$ proposed by R. H. Bing in 1950's. By the finiteness theorem \cite{Hak68}, Haken proved that can embed no compact 3-manifold. However, until now, question about whether more general space such as compact, locally connected and 1-connected metric 3-space was not known. Using techniques developed Sternfeld's 1977 PhD thesis \cite...

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptoti...

For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn , let K(Y ) be the family of all fuzzy sets of Rn , which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space K(Y ) with the topology of endograph metric is homeomorphic to the Hilbert cube Q = [−1, 1] iff Y is compact; and the space K(Y ) is homeomorphic to {(...

There is a locally compact Hausdorff space of weight אω which is linearly Lindelöf and not Lindelöf.

We formulate a conjecture that arithmetic locally symmetric manifolds have simple homotopy type, and prove it for the non-compact case. More precisely, we show that, for any symmetric space S of noncompact type without Euclidean de Rham factors, there are constants α = α(S) and d = d(S) such that any non-compact arithmetic manifold, locally isometric to S, is homotopically equivalent to a simpl...