- #1

AxiomOfChoice

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*any*constant [itex]k[/itex]?

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- Thread starter AxiomOfChoice
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- #1

AxiomOfChoice

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- #2

HallsofIvy

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- #3

AxiomOfChoice

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Point taken. Suppose we are in a vector space on which a metric has been defined.

- #4

Landau

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Let A be subset of X, and k a non-zero scalar. Then [itex]k\cdot\text{int}A=\text{int}kA[/itex].

(Use that multiplication with k is a homeomorphism. Basically, this means the topology in a TVS is scale invariant. Haven't worked out the details.)

Assuming this is true, the answer to both your questions is then 'yes'.

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