Editing Interval (mathematics) (section)

=== In general topology ===
Every [[Tychonoff space]] is embeddable into a [[product space]] of the closed unit intervals <math>[0,1].</math> Actually, every Tychonoff space that has a [[base (topology)|base]] of [[cardinality]] <math>\kappa</math> is embeddable into the product <math>[0,1]^\kappa</math> of <math>\kappa</math> copies of the intervals.<ref name="Engelking">{{cite book
|first=Ryszard
|last=Engelking
|title=General topology
|language=en
|edition=Revised and completed
|series=Sigma Series in Pure Mathematics
|volume=6
|publisher=Heldermann Verlag
|location=Berlin
|date=1989
|isbn=3-88538-006-4
|mr=1039321
|zbl=0684.54001
}}</ref>{{rp|p. 83, Theorem 2.3.23}}

The concepts of convex sets and convex components are used in a proof that every [[totally ordered set]] endowed with the [[order topology]] is [[completely normal]]<ref name="Steen" /> or moreover, [[monotonically normal]].<ref name="Heath" />