let X, Y, Z be non empty TopSpace; ( Y,Z are_homeomorphic implies oContMaps X,Y, oContMaps X,Z are_isomorphic )
given f being Function of Y,Z such that A1:
f is being_homeomorphism
; T_0TOPSP:def 1 oContMaps X,Y, oContMaps X,Z are_isomorphic
reconsider f = f as continuous Function of Y,Z by A1, TOPS_2:def 5;
take
oContMaps X,f
; WAYBEL_1:def 8 oContMaps X,f is isomorphic
thus
oContMaps X,f is isomorphic
by A1, Th21; verum