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Exercise 2. Let X be a topological space. Endow Xx X with the product topology. Consider the map f: X→ X x X, x→ (x,x). Its image f(X) is the diagonal Ax = {(x,x) | x = X}.} d) Give an example of a topological space X such that Ax is not closed in X X X. c) Endow R² edsedna to polquiszo

Exercise 2. Let X be a topological space. Endow Xx X with the product topology. Consider the map f: X→ X x X, x→ (x,x). Its image f(X) is the diagonal Ax = {(x,x) | x = X}.} d) Give an example of a topological space X such that Ax is not closed in X X X. c) Endow R² edsedna to polquiszo

Advanced Engineering Mathematics
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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Exercise 2. (Let X be a topological space. Endow X X X with the product topology. Consider the map f: X→ X x X, x(x,x). Its image f(X) is the diagonal Ax = {(x,x) | x = X}.} d) Give an example of a topological space X such that Ax is not closed in X x X. c) Endow R Xbolques edna lo esiqmuz badonnos
Transcribed Image Text:Exercise 2. (Let X be a topological space. Endow X X X with the product topology. Consider the map f: X→ X x X, x(x,x). Its image f(X) is the diagonal Ax = {(x,x) | x = X}.} d) Give an example of a topological space X such that Ax is not closed in X x X. c) Endow R Xbolques edna lo esiqmuz badonnos
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