#### Title

#### Document Type

Topology + Dynamics and Continuum Theory

#### Publication Date

6-2017

#### Publication Source

32nd Summer Conference on Topology and Its Applications

#### Abstract

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, x_{0} ∈ X and a mapping H:X ×C → X satisfying H(x, a)=x and H(x, b)=x_{0} 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

Copyright © 2017, the Authors

#### eCommons Citation

Capulín, Felix; Juarez-Villa, Leonardo; and Orozco, Fernando, "Pseudo-Contractibility" (2017). *Summer Conference on Topology and Its Applications*. 2.

https://ecommons.udayton.edu/topology_conf/2

## Comments

This document is available for download with the permission of the presenting author and the organizers of the conference. Permission documentation is on file.

Technological limitations may prevent some mathematical symbols and functions from displaying correctly in this record’s metadata fields. Please refer to the attached PDF for the correct display.