Mirhosseinkhani, Ghasem On lattices of monotonic maps and generalized topologies. (English) Zbl 1307.54003 Proc. Inst. Appl. Math. 1, No. 2, 145-152 (2012). 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) Keywords:generalized topology PDFBibTeX XMLCite \textit{G. Mirhosseinkhani}, Proc. Inst. Appl. Math. 1, No. 2, 145--152 (2012; Zbl 1307.54003)