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KOVÁR, M.
Original Title
Sequence of dualizations of topological spaces is finite.
Type
conference paper
Language
English
Original Abstract
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.
Keywords
saturated set, dual topology, compactness operator
Authors
RIV year
2002
Released
1. 1. 2002
ISBN
0-9730867-0-X
Book
Proceedings of the Ninth Prague Topological Symposium
Pages from
181
Pages to
188
Pages count
8
BibTex
@{BUT110926 }