Let be a Topological space.
a . show that for a point there is a retract
b . if is finite, and is Hausdorff with a finite amount of connected components, what is the Necessary and sufficient condition for a retract ?
thanks!!
Let be a Topological space.
a . show that for a point there is a retract
b . if is finite, and is Hausdorff with a finite amount of connected components, what is the Necessary and sufficient condition for a retract ?
thanks!!
The definition of a retract is a continuous function from X to {a} such that f(a)=a. And that pretty much nails it down for you.
For (b), assuming you mean "finite" when you write "final", think about where the points of A are distributed within the components of X.
I corrected my spelling mistake.
I still don't get under what condition I can find a retract. Isn't the fact that both A and the connected components of X are finite is enough? I'm probably missing something...
do all points of A need to be in the same component of X?
thanks