Related papers: On centered local $\pi$-bases

We establish a characterization of the well-behaved orbits of a totally Baire $G$-space of a hereditary Lindel\"of locally compact group under a mild assumption of Hausdorffness. Furthermore we give a reformulation of the proof of Glimm's…

This thesis concerns the relationship between bounded and controlled topology and how these can be used to recognise which homotopy equivalences of reasonable topological spaces are homotopic to homeomorphisms. Let $f:X\to Y$ be a…

We prove that for any circulant matrix $C$ of size $n\times n$ with the monic characteristic polynomial $p(z)$, the spectrum of its $(n-1)\times(n-1)$ submatrix $C_{n-1}$ constructed with first $n-1$ rows and columns of $C$ consists of all…

Given a compact metric space (X,d) equipped with a non-atomic, probability measure m and a real, positive decreasing function p we consider a `natural' class of limsup subsets La(p) of X. The classical limsup sets of `well approximable'…

We investigate whether an arbitrary base for a dense-in-itself topological space can be partitioned into two bases. We prove that every base for a T_3 Lindel\"of topology can be partitioned into two bases while there exists a consistent…

In this paper, some features of countably $\alpha$-compact topological spaces are presented and proven. The connection between countably $\alpha$% -compact, Tychonoff, and $\alpha$-Hausdorff spaces is explained. The space is countably…

Let $G \otimes _f H$ denote the Sierpi\'nski product of graphs $G$ and $H$ with respect to the function $f$. The Sierpi\'nski general position number ${\rm gp}{_{\rm S}}(G,H)$ is introduced as the cardinality of a largest general position…

A space $X$ is said to be $\pi$-metrizable if it has a $\sigma$-discrete $\pi$-base. In this paper, we mainly give affirmative answers for two questions about $\pi$-metrizable spaces. The main results are that: (1) A space $X$ is…

We introduce and analyze a new cardinal characteristic of the continuum, the \emph{splitting number of the reals}, denoted $\mathfrak{s}(\mathbb R)$. This number is connected to Efimov's problem, which asks whether every infinite compact…

We propose the notion of countable decomposability of maps on C*-algebras: a bounded linear map $\varphi : \mathscr{A}\to B(\mathcal{H})$, where $\mathscr{A}$ is a C*-algebra and $\mathcal{H}$ a Hilbert space, will be called countably…

Recently, Candy and Bournaveas proved local well-posedness of the space-time monopole equation in Lorenz gauge for initial data in $H^s $ with $s>\frac14$. The equation is $L^2$-critical, and hence a $\frac14$ derivative gap is left between…

We continue our investigation of cardinal sequences associated with locally Lindelof, scattered, Hausdorff P-spaces (abbreviated as LLSP spaces). We outline a method for constructing LLSP spaces from cone systems and partial orders with…

The second author has recently shown ([20]) that any selectively (a) almost disjoint family must have cardinality strictly less than $2^{\alpeh_0}$, so under the Continuum Hypothesis such a family is necessarily countable. However, it is…

Let T be the family of open subsets of a topological space (not necessarily Hausdorff or even T_0). We prove that if T has a base of cardinality <= mu, lambda <= mu < 2^lambda, lambda strong limit of cofinality aleph_0, then T has…

In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance, $\mathfrak b=\mathfrak s=\mathfrak c$…

The property of countable metacompactness of a topological space gets its importance from Dowker's 1951 theorem that the product of a normal space X with the unit interval is again normal iff X is countably metacompact. In a recent paper,…

We show that the existence of a Pi^{1}_{N}-indescribable cardinal over the Zermelo-Fraenkel's set theory ZF is proof-theoretically reducible to iterations of Mostowski collapsings and lower Mahlo operations. Furthermore we describe a…

The Proper Forcing Axiom implies that compact Hausdorff spaces are either first-countable or contain a converging $\omega_1$-sequence.

A space is said to be "almost discretely Lindel\"of" if every discrete subset can be covered by a Lindel\"of subspace. Juh\'asz, Tkachuk and Wilson asked whether every almost discretely Lindel\"of first-countable Hausdorff space has…

Given a property $P$ of subspaces of a $T_1$ space $X$, we say that $X$ is {\em $P$-bounded} iff every subspace of $X$ with property $P$ has compact closure in $X$. Here we study $P$-bounded spaces for the properties $P \in \{\omega D,…