Publication detail

Isomorphic approximations, closure spaces and comparable homeomorphic topologies

STANĚK, D. CHVALINA, J.

Original Title

Isomorphic approximations, closure spaces and comparable homeomorphic topologies

English Title

Isomorphic approximations, closure spaces and comparable homeomorphic topologies

Type

conference paper

Language

en

Original Abstract

Approximation theory based on Pawlak's rough sets uses closure operators determined by stars of subsets in a set partitions formed by an equivalence relation. In the contribution there are presented connections between closure spaces, topological spaces and it is proved that there exist different comparable isomorphic approximation Pawlak's operator on a universat set U as well as different comparable isomorphic closures on U or different comparable homeomorphic topologies in the sense of Bourbaki if and only if the underlying set U is infinite. The obntained result can serves as a criterion of the set infinity.

English abstract

Approximation theory based on Pawlak's rough sets uses closure operators determined by stars of subsets in a set partitions formed by an equivalence relation. In the contribution there are presented connections between closure spaces, topological spaces and it is proved that there exist different comparable isomorphic approximation Pawlak's operator on a universat set U as well as different comparable isomorphic closures on U or different comparable homeomorphic topologies in the sense of Bourbaki if and only if the underlying set U is infinite. The obntained result can serves as a criterion of the set infinity.

Keywords

Pawlak approximations, comparability of isomorphic closures and homeomorphic topologies.

Released

15.06.2017

Publisher

Univerzita obrany v Brně

Location

Brno

ISBN

978-80-7231-417-1

Book

MITAV 2017 (Matematika, informační technologie a aplikované vědy)

Edition number

1

Pages from

1

Pages to

13

Pages count

13

URL

Documents

BibTex


@inproceedings{BUT142174,
  author="David {Staněk} and Jan {Chvalina}",
  title="Isomorphic approximations, closure spaces and comparable homeomorphic topologies",
  annote="Approximation theory based on Pawlak's rough sets uses closure operators determined by stars of subsets in a set partitions formed by an equivalence relation. In the contribution there are presented connections between closure spaces, topological spaces and it is proved that there exist different comparable isomorphic approximation Pawlak's operator on a universat set U as well as different comparable isomorphic closures on U or different comparable homeomorphic topologies in the sense of Bourbaki if and only if the underlying set U is infinite. The obntained result can serves as a criterion of the set infinity.",
  address="Univerzita obrany v Brně",
  booktitle="MITAV 2017 (Matematika, informační technologie a aplikované vědy)",
  chapter="142174",
  howpublished="electronic, physical medium",
  institution="Univerzita obrany v Brně",
  year="2017",
  month="june",
  pages="1--13",
  publisher="Univerzita obrany v Brně",
  type="conference paper"
}