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Y is a 5. Suppose that X and Y are metric spaces and f X continuous onto function. Prove that if D is a dense subset of X, then f(D) is a dense subset of Y. Explain what happens if we do not require f to be onto.

Y is a 5. Suppose that X and Y are metric spaces and f X continuous onto function. Prove that if D is a dense subset of X, then f(D) is a dense subset of Y. Explain what happens if we do not require f to be onto.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2 ASSIGNMENT 6 Y is a 5. Suppose that X and Y are metric spaces and f X continuous onto function. Prove that if D is a dense subset of X, then f(D) is a dense subset of Y. Explain what happens if we do not require f to be onto.
Transcribed Image Text:2 ASSIGNMENT 6 Y is a 5. Suppose that X and Y are metric spaces and f X continuous onto function. Prove that if D is a dense subset of X, then f(D) is a dense subset of Y. Explain what happens if we do not require f to be onto.
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