Topology + Dynamics and Continuum Theory
32nd Summer Conference on Topology and Its Applications
Let X, Y be topological spaces and let f, g:X→ Y be mappings, we say that f is pseudo-homotopic to g if there exist a continuum C, points a, b ∈ C and a mapping H:X ×C → Y such that H(x, a)=f(x) and H(x, b)=g(x) for each x ∈ X. The mapping H is called a pseudo-homotopy between f and g. A topological space X is said to be pseudo-contractible if the identity mapping is pseudo-homotopic to a constant mapping in X. i.e., if there exist a continuum C, points a, b ∈ C, x0 ∈ X and a mapping H:X ×C → X satisfying H(x, a)=x and H(x, b)=x0 for each x ∈ X. In this talk we are going to give general facts about pseudo-homotopies and pseudocontractibility. As a consequence of these we can construct more examples of pseudo-contractible continua and non pseudo-contractible continua.
Copyright © 2017, the Authors
Capulín, Felix; Juarez-Villa, Leonardo; and Orozco, Fernando, "Pseudo-Contractibility" (2017). Summer Conference on Topology and Its Applications. 2.