Metrizability of Clifford topological semigroups

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...

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

The Structure of Topological Semigroups

The title of this address might incline one to the notion that here is to be found a small number of large theorems. To the contrary, I shall talk about a large number of small theorems. Actually, there does not exist a t this time any corpus of information to which the title "structure of topological semigroups" is in any fashion applicable. Whether such a body of theorems will ever exist is a...

Clifford modules and symmetries of topological insulators

We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of real irreducible representations of unitary symmetries in the Nambu space. ...