“Varopoulos paradigm”: Mackey property versus metrizability in topological groups

Metrizability and the Frechet-Urysohn Property in Topological Groups

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...

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...

Metrizability of Topological Semigroups on Linearly Ordered Topological Spaces

The authors use techniques and results from the theory of generalized metric spaces to give a new, short proof that every connected, linearly ordered topological space that is a cancellative topological semigroup is metrizable, and hence embeddable in R. They also prove that every separable, linearly ordered topological space that is a cancellative topological semigroup is metrizable, so embedd...

On Mackey Topologies in Topological Abelian

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