Related papers: PFA(S)[S] and Locally Compact Normal Spaces

A discrete subset $S$ of a topological group $G$ is called a {\it suitable set} for $G$ if $S\cup \{e\}$ is closed in $G$ and the subgroup generated by $S$ is dense in $G$, where $e$ is the identity element of $G$. In this paper, the…

In this article, we study harmonic symmetries on the compact locally conformally K\"{a}hler manifold $M$ of $dim_{\mathbb{C}}=n$. The space of harmonic symmetries is a subspace of harmonic differential forms which defined by the kernel of a…

In this paper, we introduce a new fractional Musielak-Sobolev space $Ws,{\Phi}x,y({\Omega})$ where ${\Omega}$ is an open subset in RN and we show some density properties of smooth and compactly supported functions in this space.

In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend…

We prove that each non-metrizable sequential rectifiable space $X$ of countable $cs^*$-character contains a clopen rectifiable submetrizable $k_\omega$-subspace $H$ and admits an open disjoint cover by subspaces homeomorphic to clopen…

We first show that, for a fixed locally compact manifold $N,$ the space $L^2(S^1,N)$ has not the homotopy type odf the classical loop space $C^\infty(S^1,N),$ by two theorems: - the inclusion $C^\infty(S^1,N) \subset L^2(S^1,N)$ is null…

We define and study the properties of $\gamma^{*}$-regular and $\gamma$-normal spaces. We also continue studying $\gamma_{o}$-compact spaces defined in [5].

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…

The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another…

We construct infinite families of non-simply connected locally conformally flat (LCF) 4-manifolds realizing rich topological types. These manifolds have strictly negative scalar curvature and the underlying topological 4-manifolds do not…

We prove that each closed locally continuum- connected subspace of a finite dimensional topological group is locally compact. This allows us to construct many 1-dimensional metrizable separable spaces that are not homeomorphic to closed…

We will study two subclasses of the class of feebly compact spaces in the class of (para)topological groups, the compact-bounded and weakly compact-bounded spaces, both introduced by J. Angoa, Y. F. Ortiz-Castillo and A. Tamariz-Mascar\'ua…

This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…

We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o-minimal structure. This fact together with the results in a previous paper implies tame dimension theory and…

We show that the space $\text{Lip}_0(\mathbb R^n)$ is the dual space of $L^{1}({\mathbb R}^{n}; {\mathbb R}^{n})/N$ where $N$ is the subspace of $L^{1}({\mathbb R}^{n}; {\mathbb R}^{n})$ consisting of vector fields whose divergence…

The idea of pairwise paracompactness was studied by many authors in a bitopological space. Here we study the same in the setting of more general structure of a bispace using the thoughts of the same given by Bose et al[2].

We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…

Let G be a complex semisimple Lie group, K a maximal compact subgroup and V an irreducible representation of K. Denote by M the unique closed orbit of G in P(V) and by O its image via the moment map. For any measure on M we construct a map…

Some new classes of compacta $K$ are considered for which $C(K)$ endowed with the pointwise topology has a countable cover by sets of small local norm--diameter.

We prove some facts about locales $L$ equipped with the Scott topology $\Omega(L)$, in particular studying a canonical frame homomorphism $\phi:\Omega(L)\to L$ which is motivated by an application to cognitive science. Such a topological…