Decomposition of topologies on lattices and hyperspaces

Costantini C., and Vitolo P.. Decomposition of topologies on lattices and hyperspaces. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1999. <http://eudml.org/doc/271751>.

@book{CostantiniC1999,
abstract = {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................................................................................471991 Mathematics Subject Classification: Primary 54B20; Secondary 06A12, 54A10.},
author = {Costantini C., Vitolo P.},
keywords = {poset; (order-)convex set; semilattice; lattice; upper topology; lower topology; decomposable topology; (order-)convex topology; locally (order-)convex topology; strong topology; strongly decomposable; topology; Scott topology; hyperspace; Vietoris topology; Hausdorff metric topology; Kuratowski convergence; Fell topology; consonant space; strongly decomposable topology; locally order convex topology; strong upper topology},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Decomposition of topologies on lattices and hyperspaces},
url = {http://eudml.org/doc/271751},
year = {1999},
}

TY - BOOK
AU - Costantini C.
AU - Vitolo P.
TI - Decomposition of topologies on lattices and hyperspaces
PY - 1999
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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................................................................................471991 Mathematics Subject Classification: Primary 54B20; Secondary 06A12, 54A10.
LA - eng
KW - poset; (order-)convex set; semilattice; lattice; upper topology; lower topology; decomposable topology; (order-)convex topology; locally (order-)convex topology; strong topology; strongly decomposable; topology; Scott topology; hyperspace; Vietoris topology; Hausdorff metric topology; Kuratowski convergence; Fell topology; consonant space; strongly decomposable topology; locally order convex topology; strong upper topology
UR - http://eudml.org/doc/271751
ER -