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On lattices of monotonic maps and generalized topologies. (English) Zbl 1307.54003

Summary: We study some properties between the lattice of all monotonic maps and the lattice of all generalized topologies on a nonempty set. We present a covariant and contravariant Galois connection between them. We also define the direct sum of two monotonic maps and characterize the direct sum; and give an interesting lower and upper bound for enlarging and restricting maps.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
26A48 Monotonic functions, generalizations
03G10 Logical aspects of lattices and related structures
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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