Compactification of a space X is compact containing as dense subspace. Magills construction for compactications fixed Tychonoff through partitions applied to derive various spaces (X;T), with set and variation in topologies 'T'. Some possible extensions mappings are obtained this regard. In extension topological group, the inverse operation should be extendable homeomorphically from base group....

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

Let (G,tau_G) be a topological group. We establish relationships between weakly almost periodic topologies on G coarser than tau_G, central idempotents in the compactification G^W, and certain ideals algebra of functions W(G). gain decompositions representations, generalizing many from literature. look at role pre-locally compact topologies, unitarizable extend or to Fourier-Stieltjes algebras ...

Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...

For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP (G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urys...

I would like to thank the organizers of the UNISA Topology Workshop, Koena Rufus Nailana and Sergio Salbany, for doing an excellent job acquiring funding, making arrangements, and especially for assembling an enthusiastic group of participants. An ordered topological space (X, τ,≤) is a set X with a topology τ and a partial order ≤. We usually assume some forms of compatibility between the topo...