Metrizability of topological groups having weak topologies with respect to good covers

The metrizability of L-topological groups

This paper studies the metrizability of the notion of L-topological groups defined by Ahsanullah. We show that for any (separated) L-topological group there is an L-pseudo-metric (L-metric), in sense of Gähler which is defined using his notion of L-real numbers, compatible with the Ltopology of this (separated) L-topological group. That is, any (separated) L-topological group is pseudo-metrizab...

Metrizability and the Frechet-Urysohn Property in Topological Groups

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

On Mackey Topologies in Topological Abelian Groups

Let C be a class of topological abelian groups and SPC denote the full subcategory of subobjects of products of objects of C. We say that SPC has Mackey coreflections if there is a functor that assigns to each object A of SPC an object τA that has the same group of characters as A and is the finest topology with that property. We show that the existence of Mackey coreflections in SPC is equival...

Free topological groups of weak P - spaces

It is known that the free topological group over the Tychonoff space X, denoted F(X), is a P space if and only if X is a P -space. This article is concerned with the question of whether one can characterize when F(X) is a weak P -space, that is, a space where all countable subsets are closed. Our main result is that F(X) is a weak P -space if and only if X is a weak P -space and every countable...