Result Details
Topographic spaces over ordered monoids
PAVLÍK, J. Topographic spaces over ordered monoids. Mathematics for applications, 2015, vol. 18053629, no. 1, p. 31-59. ISSN: 1805-3610.
Type
journal article
Language
English
Authors
Pavlík Jan, Mgr., Ph.D., IM DAAG (FME)
Abstract
A topography on a set is considered to be a collection of features described by two valuations: distance and elevation. Spaces with such structure will be studied on a general level, with generalized metric (gem) and pseudometric (pseudogem). We show many pseudogem distances and characteristics, particularly those related to the elevation function. We focus on paths in the topographic images and cohesiveness (generalized continuity) of their compositions with the elevation function. Special emphasis is also placed on the spaces arising from the digital geometry which have applications in image processing.
Keywords
generalized metric space; ordered monoid; path connectedness; topography
URL
Published
2015
Pages
31–59
Journal
Mathematics for applications, vol. 18053629, no. 1, ISSN 1805-3610
Publisher
Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
Place
Brno
DOI
BibTeX
@article{BUT128604,
author="Jan {Pavlík}",
title="Topographic spaces over ordered monoids",
journal="Mathematics for applications",
year="2015",
volume="18053629",
number="1",
pages="31--59",
doi="10.13164/ma.2015.04",
issn="1805-3610",
url="http://hdl.handle.net/11012/63087"
}
Projects
Support of Interdisciplinary Excellence Research Teams Establishment at BUT, EU, OP VK - Oblast podpory 2.3 - Lidské zdroje ve VaV, EE2.3.30.0005, start: 2012-07-01, end: 2015-06-30, completed
Departments