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Compactness in lattice-valued function spaces. (English) Zbl 1210.54014

Along the line with classical results, the author studies conditions which ensure the compactness and weak relative compactness of a set of mappings between two lattice-valued convergence spaces. He considers lattice-valued pointwise convergence and lattice-valued continuous convergence. The suitable notion of even continuity and regularity for subsets of a function space is introduced which seem to be of further interest.

MSC:

54A40 Fuzzy topology
54H12 Topological lattices, etc. (topological aspects)
06D22 Frames, locales
54C35 Function spaces in general topology
54D30 Compactness
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