Detail publikace

Sequence of dualizations of topological spaces is finite.

KOVÁR, M.

Originální název

Sequence of dualizations of topological spaces is finite.

Typ

článek ve sborníku ve WoS nebo Scopus

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

saturated set, dual topology, compactness operator

Autoři

KOVÁR, M.

Rok RIV

2002

Vydáno

1. 1. 2002

ISBN

0-9730867-0-X

Kniha

Proceedings of the Ninth Prague Topological Symposium

Strany od

181

Strany do

188

Strany počet

8

BibTex

@{BUT110926
}