is a mapping of a topological space (X,Tx) into a f (X,Tx) Remark 2 Suppose topo

Question

is a mapping of a topological space (X,Tx) into a f (X,Tx) Remark 2 Suppose topological space (Y, TY). Let f 1 TY) be the inverse image of the topology TY: f (Tr) system of all sets 1(U) l UETr) mama 1, we obtain that Problem 4 Prove the following theorem: Theorem Let f (x,Tx) (Y, TY) e a of a topological space (x, Tx) into a topological space (Y, TY). The mapping f is continuous if and only if the topology is stronger than the topology f '(r). Thanks to point 2 of Lemma 1, we obtain the "dual" form of Theorem 3

Explanation / Answer

X,Tx ----> Y,Ty

X, Tx ----> Zx , TZx

Tx is too stronger that Ty = TZx

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