If (X, τ1) and (Y, τ2) are topological spaces, f: X -> Y is a closed(or close, idk the true translation) function, A⊊Y and B⊊X are subsets, and B is a open set such that f-1(A)⊊B ; then show that(prove that) there exists a open set C⊊Y such that A⊊C and f-1(C)⊊B.
If (X, τ1) and (Y, τ2) are topological spaces, f: X -> Y is a closed(or close, idk the true translation) function, A⊊Y and B⊊X are subsets, and B is a open set such that f-1(A)⊊B ; then show that(prove that) there exists a open set C⊊Y such that A⊊C and f-1(C)⊊B.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hello, my name is Wolfgang and I have a Topology question in closed functions-open sets topic. If you help me, I will be grateful. This is my problem:
If (X, τ1) and (Y, τ2) are topological spaces, f: X -> Y is a closed(or close, idk the true translation) function, A⊊Y and B⊊X are subsets, and B is a open set such that f-1(A)⊊B ; then show that(prove that) there exists a open set C⊊Y such that A⊊C and f-1(C)⊊B.
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