# Is there an extensive 'cheat sheet' for general topology questions?

I'm looking for a collection of results in basic topology. Often I find myself working out some small detail for i.e. continuous functions, and I know I have done the same thing before, but cannot remember if the result was $=$ or just $\subseteq$ or what exact conditions the map has to have for the result to hold.

A small example: If $f\colon X\rightarrow Y$ is a continuous map and $A\subseteq Y$, then in general only $f^{-1}(\overline{A})\subseteq \overline{f^{-1}(A)}$. But if $f$ is also an open map, then $f^{-1}(\overline{A})=\overline{f^{-1}(A)}$.

Do you know a good (not necessarily small) collection of results? Most topology books cover some very elementary ones, but I never find what I'm looking for, or when I eventually find something, it would have been faster if I had actually proven it myself.

Thank you in advance.

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The resource you are searching for: it will be 10 times better than any one you find on the internet if you write it for yourself :) I'm not trying to be sarcastic, I'm just saying that it's well worth the time investment. Specifically the organization and content will be ideal for you. – rschwieb Oct 19 '12 at 20:42
I find keeping a list of definitions much more valuable. Re-deriving results until they become instinctual is actually a good thing - it means you are increasing your understanding of the subject. (I don't this is necessarily true for all subjects, but general topology is a case where almost all the basic results follow straight from the definitions.) – Thomas Andrews Oct 19 '12 at 20:47