On similarity between topologies

Artur Bartoszewicz; Małgorzata Filipczak; Andrzej Kowalski; Małgorzata Terepeta

Open Mathematics (2014)

  • Volume: 12, Issue: 4, page 603-610
  • ISSN: 2391-5455

Abstract

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Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.

How to cite

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Artur Bartoszewicz, et al. "On similarity between topologies." Open Mathematics 12.4 (2014): 603-610. <http://eudml.org/doc/269120>.

@article{ArturBartoszewicz2014,
abstract = {Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.},
author = {Artur Bartoszewicz, Małgorzata Filipczak, Andrzej Kowalski, Małgorzata Terepeta},
journal = {Open Mathematics},
keywords = {Abstract density topology; Mutually coinitial families; MB-representation; Algebra of sets with nowhere dense boundary; Quasicontinuous functions; Cliquish functions; abstract density topology; mutually coinitial families; algebra of sets with nowhere dense boundary; quasicontinuous functions; cliquish functions},
language = {eng},
number = {4},
pages = {603-610},
title = {On similarity between topologies},
url = {http://eudml.org/doc/269120},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Artur Bartoszewicz
AU - Małgorzata Filipczak
AU - Andrzej Kowalski
AU - Małgorzata Terepeta
TI - On similarity between topologies
JO - Open Mathematics
PY - 2014
VL - 12
IS - 4
SP - 603
EP - 610
AB - Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.
LA - eng
KW - Abstract density topology; Mutually coinitial families; MB-representation; Algebra of sets with nowhere dense boundary; Quasicontinuous functions; Cliquish functions; abstract density topology; mutually coinitial families; algebra of sets with nowhere dense boundary; quasicontinuous functions; cliquish functions
UR - http://eudml.org/doc/269120
ER -

References

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  9. [9] Steen L.A., Seebach J.A. Jr., Counterexamples in Topology, Dover, Mineola, 1995 Zbl1245.54001
  10. [10] Szpilrajn E., Sur une classe de fonctions de M. Sierpinski et la classe correspondante d’ensembles, Fund. Math., 1935, 24, 17–34 Zbl61.0229.01
  11. [11] Wronski S., The number of non-homeomorphic I-density topologies, In: Theory of Real Functions: XXXIV Semester in Banach Center, 482, Institute of Mathematics of Polish Academy of Sciences, 1990, 111–114 
  12. [12] Wronski S., Non-homeomorphic density topologies, Math. Slovaca, 2007, 57(4), 359–368 http://dx.doi.org/10.2478/s12175-007-0030-7 Zbl1150.54003

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