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.

Quasi-invariant measures with values in non-Archimedean fields on a group of diffeomorphisms were constructed for non-Archimedean manifolds M in [Lud96, Lud99t]. On non-Archimedean loop groups and semigroups they were provided in [Lud98s, Lud00a, Lud02b]. A Banach space over a local field also serves as the additive group and quasi-invariant measures on it were studied in [Lud03s2, Lud96c]. Thi...

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...

In this paper we introduce intuitionistic fuzzy generalized beta continuous mappings and intuitionistic fuzzy generalized beta irresolute mappings. We investigate some of their properties. Also we provide some characterization of intuitionistic fuzzy generalized beta continuous mappings and intuitionistic fuzzy generalized beta irresolute mappings. INTRODUCTION Atanassov [1] introduced the noti...

<p>In the realm of convergence spaces, generalisation topological groups is groups, and corresponding extension Pontryagin duality continuous duality. We prove that local quasi-convexity a necessary condition for group to be c-reflexive. Further, we every character locally quasi-convex.</p>

A topological group $X$ is called $duoseparable$ if there exists a countable set $S\subseteq X$ such that $SUS=X$ for any neighborhood $U\subseteq of the unit. We construct functor $F$ assigning to each (abelian) duoseparable (abelain-by-cyclic) $FX$, containing an isomorphic copy $X$. In fact, defined on category unital topologized magmas. Also we prove $\sigma$-compact locally compact abelian...

We consider the topological entropy of state space and quasi-state space homeomorphisms induced from C∗-algebra automorphisms. Our main result asserts that, for automorphisms of separable exact C∗-algebras, zero Voiculescu-Brown entropy implies zero topological entropy on the quasi-state space (and also more generally on the entire unit ball of the dual). As an application we obtain a simple de...

We investigate powerspace constructions on topological spaces, with a particular focus on the category of quasi-Polish spaces. We show that the upper and lower powerspaces commute on all quasi-Polish spaces, and show more generally that this commutativity is equivalent to the topological property of consonance. We then investigate powerspace constructions on the open set lattices of quasi-Polis...

We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite group G, and a 3-cocycle ω, which was first studied by Dijkgraaf, Pa...