Problem 2.39. Let X be a space and Y c X. Give Y the subspace topology. Let ACY. The notation A is ambiguous. Do we mean the closure of A in the original space X or the closure of A in the subspace Y? Show by erample that this is really ambiguous. Second point: Find a good disambiguating notational solution.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Solve 2.39

Problem 2.39. Let X be a space and Y C X. Give Y the subspace topology. Let A CY.
The notation A is ambiguous. Do we mean the closure of A in the original space X or the
closure of A in the subspace Y? Show by example that this is really ambiguous. Second
point: Find a good disambiguating notational solution.
Transcribed Image Text:Problem 2.39. Let X be a space and Y C X. Give Y the subspace topology. Let A CY. The notation A is ambiguous. Do we mean the closure of A in the original space X or the closure of A in the subspace Y? Show by example that this is really ambiguous. Second point: Find a good disambiguating notational solution.
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