In this paper we give some characterizations of topological extreme amenability. Also we answer a question raised by Ling [5]. In particular we prove that if T is a Borel subset of a locally compact semigroup S such that M(S)* has a multiplicative topological left invariant mean then T is topological left lumpy if and only if there is a multiplicative topological left invariant mean M on M(S)* ...

In this proposal, we discuss several non-classical frameworks, and their applications in epistemic modal logic. We largely consider topological semantics, as opposed to widely used Kripke semantics, paraconsistent systems, as opposed to consistent systems, and non-well-founded sets, as opposed to ZF(C) set theory. We discuss topological public announcement logics, introduce homotopies to modal ...

This paper describes non-manifold offsetting operations that add or remove a uniform thickness from a given non-manifold topological model. The mathematical definitions and properties of the non-manifold offsetting operations are investigated first, and then an offset algorithm based on the definitions is proposed and implemented using the non-manifold Euler operators proposed in this paper. In...

We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two dimensional free non-Abelian gauge theory having no interaction with matter fields. The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants ...

We address two properties for Abelian topological groups: “every closed subgroup is dually closed” and “every closed subgroup is dually embedded.” We exhibit a pair of topological groups such that each has both of the properties and the product has neither, which refutes a remark of N. Noble. These examples are the additive group of integers topologized with respect to a convergent sequence as ...

We discuss the formation of nontopological solitons in a second-order phase transition in the early Universe. Ratios of dimensionless coupling constants in the Lagrangian determine their abundance and mass. For a large range of parameters, non-topological solitons can be cosmologically significant, contributing a significant fraction of the present mass density of the Universe. Submitted to Phy...

A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin braid group – the mathematical basis of topological quantum computation (TQC). Vector spaces of TQC correspond to associated strings of particle int...

In this paper, the concept of {sl local base with  stratifiedstructure} in $I$-topological vector spaces is introduced. Weprove that every $I$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of $I$-topological vector spaces by means of thelocal base with stratified structure is given.

This paper provides necessary and sufficient conditions for the existence of solutions for some important problems from optimization and non-linear analysis by replacing two typical conditions—continuity and quasiconcavity with a unique condition, weakening topological vector spaces to arbitrary topological spaces that may be discrete, continuum, non-compact or non-convex. We establish a single...