I need to show all fxn f: X -> X are cts in the discrete top. and that the only cts fxns in the concrete top are the csnt fxns.(adsbygoogle = window.adsbygoogle || []).push({});

Let (X,T) be a discrete top with T open sets.

Let f: X->X. WTS that f:X->X is cts if for every open set G in the image of X, f^-1(G) = V is an open in X when V is a subset of X.

Since (X,T) is a discrete top, V in the power set of X must be open. Since T is open and T = PX this implies that f is cts.

Is there anything wrong with that?

As for the xecond half, i'm not sure. When they say cnst fxns do they mean f(c) = c?

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# Homework Help: Continuity homework help

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