Weak selections and pseudocompactness

Abstract

Abstract. We prove that every pseudocompact space that admits a weak selection is sequentially compact.

Coarser Compact Topologies

“…Having already established this, we can use each pseudocompact space with a continuous weak selection is sequentially compact [1,3,21], see also [6,Corollary 3.9]. Accordingly, C [X] is sequentially compact.…”

“…Proof of Theorem 6.1. Each pseudocompact space X with a continuous weak selection is suborderable, see [1,3,21]; also [6,Theorems 3.7 and 3.8]. Moreover, by Proposition 4.3, each suborderable quasi-king space is compact.…”

Asymptotically equivalent functions and ultrafilters applied to noncommutative quantum cosmology

“…As a demonstration for the functionality of the method, we will apply in the dynamical system derived from EHJ equation that comes from the FLRW metric, considering the noncommutativity in the space co-arXiv:1804.08041v3 [gr-qc] 14 Feb 2019 ordinates. In addition, together with the mentioned method we associate in the Noncommutative coordinate and momentum (NCCM)-KS Cosmology a particular family of subsets, called Ultrafilter, that is relevant in some branches of mathematics, like topology where in many cases are used to construct examples and counter examples [19,20], functional analysis and dynamical systems when discrete systems are studied [21,22]. The study of cosmology in some limits (asymptotic analysis), is well known and appears in problems related with the cosmological constant [23,24], the behavior near and far from an initial singularity in certain kinds of cosmologies [25,26] and in quintessence models [27].…”