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

✍ Scribed by Tomasz Kubiak; Iraide Mardones-Pérez

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 289 KB
• Volume: 144
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(03)00300-2

✦ Synopsis

Spaces in which open sets take values in the L-interval I(L) are investigated. We prove a theorem concerning the insertion of a continuous function with values in I(L) with L a complete lattice. We establish certain factorizations of the functors ! I(L) and -I(L) with L a hypercontinuous lattice. The latter result and the insertion theorem provide a partial answer to a recent open question related to insertion of lattice-valued functions. As another application of the insertion theorem we establish a relation between complete regularity in the categories of L-topological and I(L)-topological spaces with L a frame.