# 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

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top## Abstract

top## How to cite

topArtur 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] Steen L.A., Seebach J.A. Jr., Counterexamples in Topology, Dover, Mineola, 1995 Zbl1245.54001
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