Contractible spaces
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Let X be a contractible space:
a) Show that X is path connected
b) Show that any two continuous maps where Y is any topological space, are homotopic.
c) Let and be the map defined by . Show that and are homotopic.
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Solution Summary
This solution is comprised of a detailed explanation to
a) Show that X is path connected
b) Show that any two continuous maps where Y is any topological space, are homotopic.
c) Let and be the map defined by . Show that and are homotopic.
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Let X be a contractible space:
a) Show that X is path connected
b) Show that any two continuous maps where Y is any topological space, are homotopic.
c) Let and be the map defined by . Show that and are homotopic
Solution:
[Recall: If f and g are continuous maps of the space X into space Y, we say f is homotopic to g if there is another continuous map
F: X x I Y such that
F(x,0) = f(x) and F(x,1) = g(x) for each x in X.
(here I = [0,1]). The map F is called as the homotopy between f and g. we write this as f g. If f is a ...
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