Sequence of dualizations of topological spaces is finite.

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F02%3APU22441" target="_blank" >RIV/00216305:26220/02:PU22441 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Sequence of dualizations of topological spaces is finite.
Original language description
Problem 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 was for $T_1$ spaces 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 $(X,tau)$ it follows $tau^{dd}=tau^{dddd}$. Further, we classify topological spaces with respect to the number of generated topologies by the process of taking duals.
Czech name
—
Czech description
—

Project
—
Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju<br>N - Vyzkumna aktivita podporovana z neverejnych zdroju

Publication year
2002
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the Ninth Prague Topological Symposium
ISBN
0-9730867-0-X
ISSN
—
e-ISSN
—
Number of pages
8
Pages from-to
—
Publisher name
Neuveden
Place of publication
Neuveden
Event location
Praha
Event date
Aug 19, 2001
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—

Similar results(10)