Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3643
Articles: 2'487'895
Articles rated: 2609

29 March 2024
 
  » arxiv » math.GN/0204132

 Article overview


Sequence of dualizations of topological spaces is finite
Martin Maria Kovar ;
Date 10 Apr 2002
Journal Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 171--179, Topology Atlas, Toronto, 2002}
Subject General Topology MSC-class: 54B99, 54D30, 54E55 | math.GN
AbstractProblem 540 of J. D. Lawson and M. Mislove in Open Problems in Topology asks whether the process of taking duals terminate after finitely many steps with topologies that are duals of each other. The problem for $T_1$ spaces was already solved by G. E. Strecker in 1966. For certain topologies on hyperspaces (which are not necessarily $T_1$), the main question was in the positive answered by Bruce S. Burdick and his solution was presented on The First Turkish International Conference on Topology in Istanbul in 2000. In this paper we bring a complete and positive solution of the problem for all topological spaces. We show that for any topological space $(X, au)$ it follows $ au^{dd}= au^{dddd}$. Further, we classify topological spaces with respect to the number of generated topologies by the process of taking duals.
Source arXiv, math.GN/0204132
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser claudebot






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica