sierpinski space is contractible - Let X be Sierpinski space: X={x,y} with topology {X,empty set, {x}} .
prove that X is contractible.
Contractible spaces - (See attached file for full problem description with all symbols)
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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 topo ...
Nullhomotopic Mappings and Contractible Spaces - I am having problems proving this fact. A space X is contractible if and only if
every map f:X to Y (Y is arbitrary) is nullhomotopic. Similarly show X is contractible
iff ever map f:Y to X is nullh ...
Metric space proofs - This problem is from Metric Space. Please give a formal proof based on the reference provided.
Given a metric space (X,p), prove that...