Non-continuous fundamental groups of continuous loops

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Stephen S. Andersen (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Hughes Hoyle

Abstract: Let (Y,T) be a topological space, let y0 ? Y, and let C(Y,y0) denote the set of continuous loops in Y at y0. It has long been known that using continuous functions as relating functions on C(Y,y0) produces an equivalence relation on C(Y,y0), and that there is a natural binary operation on the resulting equivalence classes which makes the equivalence classes a group - called the fundamental group of Y at y0, denoted by TT1(Y,y0). In this thesis another type of relating functions, the class of which we call an admitting homotopy relation, is defined and it is shown that these functions also produce a group, which we call the N-fundamental group of Y with respect to y0, denoted by N(Y,y0). It is shown that this group satisfies the usual properties of the fundamental group, and that given a topological space (Y, T) and y0 ? Y, there is an epimorphism from TT1 (Y,y0) onto N(Y,y0).

Additional Information

Language: English
Date: 1976
Loops (Group theory)
Topological spaces
Homotopy theory

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