We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes with the homotopy type of an Eilenberg-MacLane space K(π, 1) equipped with a cellular self-map of prime order. As an application we derive the section conjecture for the real points of aspherical varieties defined over the field of real numbers and the natural an...

The set of all closed subgroups of a profinite carries a natural profinite topology. This space of subgroups can be classified up to homeomorphism in many cases, and tight bounds placed on its complexity as expressed by its scattered height.

The theory of profinite groups is flourishing! This is the first immediate observation from looking at the four books on the subject which have come out in the last two years. The subject, which only two decades ago was somewhat remote, has made its way to mainstream mathematics in several different ways. What is a profinite group? A profinite group G is a topological group which is Hausdorff, ...

Let X be a connected scheme. Then one can associate (after Grothendieck) to X its algebraic fundamental group π1(X). This group π1(X) is a profinite group which is uniquely determined (up to inner automorphisms) by the property that the category of finite, discrete sets equipped with a continuous π1(X)-action is equivalent to the category of finite étale coverings of X. Moreover, the assignment...

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 S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

We study profinite completion of spaces in the model category of profinite spaces and construct a rigidification of the completion functors of Artin-Mazur and Sullivan which extends also to non-connected spaces. Another new aspect is an equivariant profinite completion functor and equivariant fibrant replacement functor for a profinite group acting on a space. This is crucial for applications w...

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.

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

This paper applies a combination of algebraic and topological methods to obtain new structural results on mp- purified residuated lattices. It is demonstrated that mp-residuated lattices are strongly tied up with the dual hull-kernel topology. Mainly, it shown lattice mp if only its minimal prime spectrum, equipped topology, Hausdorff fitted normal. For $${\mathfrak {A}}$$ subalgebra {S}}$$ , n...