reconsider T = TOP-REAL n as SubSpace of TOP-REAL n by TSEP_1:2;
take T ; :: thesis: ( T is strict & not T is empty & T is convex )
thus ( T is strict & not T is empty ) ; :: thesis: T is convex
thus [#] T is convex Subset of (TOP-REAL n) by JORDAN2C:21; :: according to TOPALG_2:def 1 :: thesis: verum