Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
An Equivalence Of Shape And Deck Groups; Further Classification Of Sharkovskii Groups, Tyler Willes Hills
An Equivalence Of Shape And Deck Groups; Further Classification Of Sharkovskii Groups, Tyler Willes Hills
Theses and Dissertations
In part one we show that for a compact, metric, locally path-connected topological space X, the shape group of X - as defined in Foundations of Shape Theory by Mardesic and Segal - is isomorphic to the inverse limit of discrete homotopy groups introduced by Conrad Plaut and Valera Berestovskii. We begin by providing the reader preliminary definitions of the fundamental group of a topological space, inverse systems and inverse limits, the Shape Category, discrete homotopy groups, and culminate by providing an isomorphism of the shape and deck groups for peano continua. In part two we develop work and provide …
Regular Fibrations Over The Hawaiian Earring, Stewart Mason Mcginnis
Regular Fibrations Over The Hawaiian Earring, Stewart Mason Mcginnis
Theses and Dissertations
We present a family of fibrations over the Hawaiian earring that are inverse limits of regular covering spaces over the Hawaiian earring. These fibrations satisfy unique path lifting, and as such serve as a good extension of covering space theory in the case of nonsemi-locally simply connected spaces. We give a condition for when these fibrations are path-connected.