reserve a, r, s for Real;

theorem Th17:
  r <= s implies Closed-Interval-TSpace(r,s) is locally_connected
proof
  assume r <= s;
  then ex B being Basis of Closed-Interval-TSpace(r,s) st (ex f being
  ManySortedSet of Closed-Interval-TSpace(r,s) st for y being Point of
Closed-Interval-MSpace(r,s) holds f.y = {Ball(y,1/n) where n is Nat:
n <> 0} & B = Union f) & for X being Subset of Closed-Interval-TSpace(r,s) st X
  in B holds X is connected by Th2;
  hence thesis by Th16;
end;
