Metrizability of ordered additive 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...

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...

Metrizability and the Frechet-Urysohn Property in Topological Groups

Characterizing automorphism groups of ordered abelian groups

In this short note we want to characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of abelian groups, see [2]. Recall that H is a right ordered group (RO-group) if (H, ·) is a group and (H,<) is a linear order satisfying...

Ordered O-stable Groups

An ordered structure M is called o-λ-stable if for any subset A with |A| ≤ λ and for any cut in M there are at most λ 1-types over A which are consistent with the cut. It is proved in the paper that an ordered o-stable group is abelian. Also there were investigated definable subsets and unary functions of o-stable groups.