Description: If a continuous mapping to a T_1 space is constant on a dense subset, it
is constant on the entire space. Note that
( ( clsJ )A ) = X means " A is dense in X " and
A C_ (`' F " { P } ) means " F is constant on A ` " (see
funconstss ). (Contributed by NM, 15-Mar-2007)(Proof shortened by Mario Carneiro, 21-Aug-2015)