Let f:(X,τX)→(Y,τY) be a continuous function between topological spaces. Can you show that
U,V∈τY, U∩V=∅⟹f−1(U)∩f−1(V)=∅.
It is stated as a fact in a proof that path-connectedness implies connectedness.
Thursday, 22 November 2018
elementary set theory - Intersection of images is empty implies intersection of preimages is empty.
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