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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}.} b) Show that f is a homeomorphism on its image f(X) = Ax, i.e. the restriction f : X→ Ax is a homeomorphism.

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}.} b) Show that f is a homeomorphism on its image f(X) = Ax, i.e. the restriction f : X→ Ax is a homeomorphism.

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 XXX 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}.} b) Show that f is a homeomorphism on its image f(X) = Ax, i.e. the restriction f : X→ Ax is a homeomorphism. c) Endow R² songe Kon enshary murrixsMarq0S saiutos dos ai 8 A edsedna lo esiqmazs vid I badonnos
Transcribed Image Text:Exercise 2. Let X be a topological space. Endow XXX 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}.} b) Show that f is a homeomorphism on its image f(X) = Ax, i.e. the restriction f : X→ Ax is a homeomorphism. c) Endow R² songe Kon enshary murrixsMarq0S saiutos dos ai 8 A edsedna lo esiqmazs vid I badonnos
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