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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  1. [1] Aniszczyk B., Frankiewicz R., Nonhomeomorphic density topologies, Bull. Polish Acad. Sci. Math., 1986, 34(3–4), 211–213 Zbl0591.54002
  2. [2] Balcerzak M., Bartoszewicz A., Ciesielski K., Algebras with inner MB-representation, Real Anal. Exchange, 2003/04, 29(1), 265–273 Zbl1065.03033
  3. [3] Balcerzak M., Bartoszewicz A., Rzepecka J., Wronski S., Marczewski fields and ideals, Real Anal. Exchange, 2000/01, 26(2), 703–715 Zbl1009.28001
  4. [4] Burstin C., Eigenschaften meßbaren und nichtmeßbaren Mengen, Akademie der Wissenschaften in Wien, 1914, 123, 1525–1551 
  5. [5] Filipczak M., Wagner-Bojakowska E. (Eds.), Traditional and Present-Day Topics in Real Analysis, Łódz University Press, Łódz, 2013 
  6. [6] Hejduk J., One more difference between measure and category, Tatra Mt. Math. Publ., 2011, 49, 9–15 Zbl1265.54013
  7. [7] Lipinski J.S., Šalát T., On the points of quasicontinuity and cliquishness of functions, Czechoslovak Math. J., 1971, 21(96), 484–489 Zbl0219.26004
  8. [8] Pawlikowski J., Parametrized Ellentuck theorem, Topology Appl., 1990, 37(1), 65–73 http://dx.doi.org/10.1016/0166-8641(90)90015-T Zbl0734.04001
  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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