Cones, semicontinuous functions, and continuous lattices
type: Item
instance of: scholarly article
title: Cones, semicontinuous functions, and continuous lattices
zbMATH Open document ID: 0613.06005
DOI: 10.1007/BF00400293
author: John A. Tiller
published in: Order
publication date: 1986-01-01T00:00:00Z
review text: Standard examples of continuous lattices are spaces of lower semicontinuous functions. In this paper the author introduces a generalization, which he calls a star, of a star-shaped set in a vector space. He shows that the lattice of closed star-shaped subsets for some fixed nucleus is a continuous lattice if the star is compact, and that the lattice of lower semicontinuous functions from a locally compact Hausdorff space to [0,1] can be characterized as the lattice of substars of a compact star from a certain natural class of compact stars.
reviewed by: Jimmie D. Lawson
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 3991562
zbMATH Keywords: continuous lattices
zbMATH Keywords: lower semicontinuous functions
zbMATH Keywords: star-shaped set
zbMATH Keywords: lattice of closed star-shaped subsets
zbMATH Keywords: lattice of substars
zbMATH Keywords: compact star
MaRDI profile type: Publication
cites work: Q3898534
cites work: Q3961473
full work available at URL: https://doi.org/10.1007/bf00400293
OpenAlex ID: W2068434389
description: scientific article; zbMATH DE number 3991562