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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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