A note on induced and coinduced fuzzy topologies

Abstract

In this note we lay down criteria for the ‘goodness’ (following Lowen) of definitions of induced and coinduced fuzzy topologies. Both are known (under different terminology) to be good. In the case of induction we give an alternative proof to that of Lowen, using basic open sets in fuzzy topological spaces, thus providing a simple fuzzy topological proof of the extension theorem for lower semi-continuous functions.