Katětov-Tong insertion theorem for functions with values in a tensor product of complete lattices

Abstract

It is shown that Katětov-Tong insertion theorem continues to hold for normal L-topological spaces and functions with values in appropriately L-topologized tensor product where L is a complete lattice with an order-reversing involution and M is a completely distributive lattice with a countable join base free of supercompact elements. When the first factor is the real unit interval, the tensor product can be identified with the Hutton fuzzy unit interval. Among corollaries of our insertion theorem are Urysohn lemma and Tietze extension theorem for -valued functions as well as Katětov-Tong insertion theorem for M-valued functions on traditional topological spaces.