let h be Function of T,(TOP-REAL n); :: thesis: ( h = f [#] r implies h is continuous )
assume A2: h = f [#] r ; :: thesis: h is continuous
reconsider r = r as Element of R^1 by XREAL_0:def 1;
dom f = the carrier of T by FUNCT_2:def 1;
then h = f <#> (T --> r) by A2, Th31;
hence h is continuous ; :: thesis: verum