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Convex Subsets

Meital
in Linear Algebra and Group Theory

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If X is a linear continuum space how do we show that all convex

subsets of X must inheret the linear contiuum axioms, that is, they

have betweenness and least upper bound property. Thanks.

  • 4 months later...

Thats a deep question. Are you studying foundations? I had a great little book once by Paul Cohen where he proved that the continuum hypothesis is optional as an axiom. I loned it to an undergrad and never saw it again.

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