Question

Let X, Y be topological spaces, where X is compact and Y is Hausdorff. Let f be a continuous function in Homtop(X, Y). Then, we have cl(f(A)) = f(cl(A)). To prove this, we need to show that each set is contained in the other. How can we do this without using series, but only relying on the definitions of continuity, properties, Hausdorff, and compactness?

Name: let x y be topological spaces where x is compact and y is hausdorff let f be a continuous function in homtopx y then we have clfa fcla to prove this we need to show that each set is containe 81408
Uploaded: 2023-03-16T07:08:33-08:00
Duration: 2 min 15 s
Channel: Sri K
Description: let x y be topological spaces where x is compact and y is hausdorff let f be a continuous function in homtopx y then we have clfa fcla to prove this we need to show that each set is containe 81408

          Let X, Y be topological spaces, where X is compact and Y is Hausdorff. Let f be a continuous function in Homtop(X, Y). Then, we have cl(f(A)) = f(cl(A)). To prove this, we need to show that each set is contained in the other. How can we do this without using series, but only relying on the definitions of continuity, properties, Hausdorff, and compactness?

Added by Jose Manuel B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/16/2023

Step 1

Step 1: First, let's show that cl(f(A)) is contained in f(cl(A)). Show more…

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Let X, Y be topological spaces, where X is compact and Y is Hausdorff. Let f be a continuous function in Homtop(X, Y). Then, we have cl(f(A)) = f(cl(A)). To prove this, we need to show that each set is contained in the other. How can we do this without using series, but only relying on the definitions of continuity, properties, Hausdorff, and compactness?