A Pro-algebraic Fundamental Group for Topological Spaces

The Fundamental Algebraic Group of Topological Spaces

In the study of topology, we are often interested in understanding and classifying the internal structure of topological spaces. Algebraic topology is the application of abstract algebra to topology in order to further identify the structure of topological spaces by developing a correspondence between topological spaces and certain groups called homotopy groups. In this paper, we will examine t...

Optimization in Algebraic and Topological Vector Spaces

Some Characterizations of Hopf Group on Fuzzy Topological Spaces

In this paper, some fundamental concepts are given relating to fuzzytopological spaces. Then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. Also the fuzzy topological spaces which are Hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...

Algebraic Topology Notes, Part Ii: Fundamental Group

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Algebraic fundamental group and simplicial complexes

In this paper we prove that the fundamental group of a simplicial complex is isomorphic to the algebraic fundamental group of its incidence algebra, and we derive some applications. AMS classification : 16E40 ; 16G20 ; 06A11 ; 55Q05 Let k be a field and A be a basic and split finite dimensional k-algebra, which means that A/r = k× k× . . .× k where r is the radical of A. There exists a unique q...