An insertion theorem for continuous \(\mathbb I(L)\)-valued functions and its consequences (Q1876512)

The work deals with a generalisation of the insertion theorem, i.e. the problem of inserting a continuous function between two comparable functions. The direction of the generalisation is from the two-point lattice \(\{ 0, 1\}\) to an arbitrary complete lattice \((L,')\) or, more precisely, from \({\mathbb{I}}(\{ 0,1\})\) to Hutton's \(L\)-interval \(\mathbb I(L)\). The results achieved for the insertion problem lead to consequences for a relation between complete regularity in the categories of \(L\)-topological and \(\mathbb I(L)\)-topological spaces with \(L\) a frame.