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12:42 PM
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A: Overview of basic results about images and preimages

Martin SleziakI have no doubt that you there are many useful online resources for these, but many such results are available here at MSE, together with their proofs. I'll give a list of some basic results about images and preimages links to the posts, which have proofs here at MSE. I am making this CW, so fee...

Is there a similar list for stronger results when the map is continuous? — plebmatician 30 mins ago
I am not sure what the user who posted the above comment means - for example, I cannot imagine something I can specifically say about $f[A\cap B]$ if I have the additional assumptions that the function is continuous.
Perhaps properties like this are mean in that comment: preimage of an open set (under continuous function) is open, continuous image of a compact set is compact, continuous image of a compact set is compact.
I am posting this here in case somebody might have an idea what is actually meant here.
@plebmatician To be honest, I am not really sure what kind of properties you have in mind. In any case, I have mentioned this in Calculus and analysis chatroom, maybe somebody will notice it there. — Martin Sleziak 11 secs ago
 

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