How does functions affect closure

[Cratylus]

Looked around and couldn’t get much help so this is my best guess

I am thinking if we have a closed function on some set A and take it’s preimage and if this preimage is closed.We have a closure ? I base my idea of the above the theorem.

Source A first course in Topology:Conover

 

[pka]

Looked around and couldn’t get much help so this is my best guess
I am thinking if we have a closed function on some set A and take it’s preimage and if this preimage is closed.We have a closure ? I base my idea of the above the theorem.

Your post makes me wonder if you understand open/closed mappings? HERE is a good summery.
Frankly, I do not know what is your question. Can you please tell us?

 

[Cratylus]

Your post makes me wonder if you understand open/closed mappings? HERE is a good summery.
Frankly, I do not know what is your question. Can you please tell us?

I am not proving anything.
How do functions affect closure?

l have this theorem
Let X and Y be topological spaces and let f X:[MATH]\mapsto[/MATH] Y. Then f is continuous
on X whenever F is a closed set in Y, then f [MATH]^{-1}[/MATH](F) is closed in Y

A function f:X[MATH]\mapsto[/MATH]Y is a closed function if whenever F is closed in X then f(F) is closed in Y

I was thinking this describes part of closure but not sure what to do after that,which is
what I stated what I said. I am used to dealing with sets and closure.

 

[pka]

I am not proving anything. How do functions affect closure?

Functions do not affect closure. If \(X~\&~Y\) are top-spaces and \(f:X\to Y\) then
\( f\) is a closed function if and only if the image of each closed set in \(X\) is a closed in \(Y\).

 

[Cratylus]

Functions do not affect closure. If \(X~\&~Y\) are top-spaces and \(f:X\to Y\) then
\( f\) is a closed function if and only if the image of each closed set in \(X\) is a closed in \(Y\).

I guess it could of been a trick question.Thanks

 

[pka]

I guess it could of been a trick question. Thanks

I have ask you more than once to study from a recognized topology textbook.
There are many such books on the used book market for little money.

 

[Cratylus]

I have ask you more than once to study from a recognized topology textbook.
There are many such books on the used book market for little money.

I have Bert Mendelson. l plan to get Croom’s one day