Convex Subsets

[Meital]

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.

[ElijahJones]

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.