reserve r,s,t,u for Real;

theorem Th49:
  for X being LinearTopSpace, V being open Subset of X, r being
  non zero Real holds r*V is open
proof
  let X be LinearTopSpace, V be open Subset of X, r be non zero Real;
   reconsider r as non zero Real;
  mlt(r,X).:V = r*V by Th46;
  hence thesis by TOPGRP_1:25;
end;
