Previously, the authors used insights of Robinson's nonstandard analysis as a powerful tool to extend and simplify construction some compactifications regular spaces. They now show that any Hausdorff compactification is obtainable with their method.

Abstract In order to improve the physical adsorption of composite curing agent and solidification treatment effect waste mud, materials processes were studied. Through study orthogonal experiments, effects polyvinyl alcohol (PVA) concentration, spinning voltage, distance other factors on diameter, fibre uniformity morphology PVA nanofibers explored, with optimal preparation conditions for The p...

Quasi-abelian categories are abundant in functional analysis and representation theory. It is known that a quasi-abelian category $\mathcal{E}$ cotilting torsionfree class of an abelian category. In fact, this property characterizes categories. This ambient derived equivalent to the $\mathcal{E}$, can be constructed as heart $\mathcal{LH}(\mathcal{E})$ $t$-structure on bounded $\mathbf{D}^b(\ma...

This document is a summary of basic facts about the “standard” category of compactly generated spaces introduced by McCord [McC69] (often referred to in the literature as “compactly generated weak Hausdorff spaces”, or “weak Hausdorff k-spaces”). The main references I’ve used for this material are Gaunce Lewis’s thesis [Lew, App. A], and Neil Strickland’s note [Str09] (especially for material a...

Rendering quality is largely influenced by the samplers used in Monte Carlo integration. Important factors include sample uniformity (e.g., low discrepancy) high-dimensional integration domain, lower-dimensional projections, and lack of dominant structures that could result aliasing artifacts. A widely successful construction Sobol' sequence guarantees good consequently results faster convergen...

in this paper we establish a characterization of abelian compact hausdorff semigroups with unique idempotent and ideal retraction property. we also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

In [5] Todorčević shows that there is no Hausdorff gap (A,B) if A is analytic. In this note we extend the result by showing that the assertion “there is no Hausdorff gap (A,B) if A is coanalytic” is equivalent to “there is no Hausdorff gap (A,B) if A is Σ2”, and equivalent to ∀r (א L[r] 1 < א1). We also consider real-valued games corresponding to Hausdorff gaps, and show that ADR for pointclass...

‎recently‎, ‎hussain et al.‎, ‎discussed the concept of $wt$-distance on a‎ ‎metric type space‎. ‎in this paper‎, ‎we prove some fixed‎ ‎point theorems for classes of contractive type multi-valued operators‎, ‎by using $wt$-distances in the setting of a complete metric type space‎. ‎these results generalize a result of feng and liu on multi-valued operators.

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...