Detail publikačního výsledku

At most 4 topologies can arise from iterating the de Groot dual

KOVÁR, M.

Originální název

At most 4 topologies can arise from iterating the de Groot dual

Anglický název

At most 4 topologies can arise from iterating the de Groot dual

Druh

Článek recenzovaný mimo WoS a Scopus

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 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 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.

Anglický 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 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 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

Klíčová slova v angličtině

saturated set, dual topology, compactness operator

Autoři

KOVÁR, M.

Rok RIV

2011

Vydáno

01.05.2003

ISSN

0166-8641

Periodikum

TOPOLOGY AND ITS APPLICATIONS

Svazek

2003

Číslo

130

Stát

Nizozemsko

Strany od

175

Strany do

182

Strany počet

8

BibTex

@article{BUT41534,
  author="Martin {Kovár}",
  title="At most 4 topologies can arise from iterating the de Groot dual",
  journal="TOPOLOGY AND ITS APPLICATIONS",
  year="2003",
  volume="2003",
  number="130",
  pages="175--182",
  issn="0166-8641"
}