Suppose that $ X $ and $ Y $ are topological spaces, and $ Y $ is a Hausdorff space. Suppose that $ A $ is a subset of $ X $ and $\overline{A} = X$. Suppose that $ f : X \to Y $ and $ g : X \to Y $ are continuous functions, and $ f(a) = g(a) $ for all $ a \in A $. Prove that $ f(x) = g(x) $ for all $ x \in X $.

Given, X and Y are topological spaces, and Y is a Hausdorff space. Let A⊂X and A=X. Suppose that…

Suppose that X and Y are topological spaces, and Y is a Hausdorff space. Suppose that A is a subset of X and A = X. Suppose that f : X → Y and g : X → Y are continuous functions, and f(a) = g(a) for all a E A. Prove that f(x) = g(x) for all x E X.

Suppose that X and Y are topological spaces, and Y is a Hausdorff space. Suppose that A is a subset of X and A = X. Suppose that f : X → Y and g : X → Y are continuous functions, and f(a) = g(a) for all a E A. Prove that f(x) = g(x) for all x E X.

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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Suppose that $ X $ and $ Y $ are topological spaces, and $ Y $ is a Hausdorff space. Suppose that $ A $ is a subset of $ X $ and $\overline{A} = X$. Suppose that $ f : X \to Y $ and $ g : X \to Y $ are continuous functions, and $ f(a) = g(a) $ for all $ a \in A $. Prove that $ f(x) = g(x) $ for all $ x \in X $.

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