AbstractThe notion of decomposable topology is introduced in a partially ordered set and, in particular, in the lattice C(X) of all closed subsets (ordered by reverse inclusion) of a topological space X, which is also called the hyperspace of X. This notion is closely related to the concepts, defined in the same framework, of lower, upper and strong upper topology.We investigate decomposability and unique decomposability of the main hyperspace topologies, and of topologies which are defined on some quite natural lattices or semilattices.
CONTENTSIntroduction.................................................................................51. Decomposable topologies.......................................................62. Locally convex topologies......................................................103. Semilattices. Strong decomposability.....................................134. Convex topologies.................................................................155. Topologies on linearly ordered sets.......................................186. Topologies on lattices............................................................207. The Scott topology.................................................................268. Uniqueness of decomposition................................................289. Hyperspace topologies..........................................................3210. The Vietoris topology...........................................................3511. The Hausdorff metric topology.............................................3712. The proximal topology..........................................................3913. The Kuratowski convergence..............................................4014. Uniqueness of decomposition for hypertopologies..............44References................................................................................47
1991 Mathematics Subject Classification: Primary 54B20; Secondary 06A12, 54A10.
@book{bwmeta1.element.zamlynska-7e320ad6-fffd-428f-8383-035e35f24602,
author = {Costantini C. and Vitolo P.},
title = {Decomposition of topologies on lattices and hyperspaces},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1999},
zbl = {0965.54015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-7e320ad6-fffd-428f-8383-035e35f24602}
}
Costantini C.; Vitolo P. Decomposition of topologies on lattices and hyperspaces. GDML_Books (1999), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-7e320ad6-fffd-428f-8383-035e35f24602/