Publication detail

Jordan curve theorems with respect to certain pretopologies on Z^2

ŠLAPAL, J.

Czech title

Věty o Jordanových křivkách vzhledem k jistým pretopologiím na Z^2

English title

Jordan curve theorems with respect to certain pretopologies on Z^2

Type

journal article - other

Language

en

Original abstract

We discuss four quotient pretopologies of a certain basic topology on the digital plane. Three of them are even topologies and include the well-known Khalimsky and Marcus-Wyse topologies. Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies.

Czech abstract

Jsou studovány čtyři faktorové pretopologie jisté základní topologie na digitální rovině. Tři z nich jsou dokonce topologiemi a zahrnují dobře známé Khalimského a Marcus-Wiseho topologie. Známé Jordanovy křivky v základní topologii jsou užity pro nalezení Jordanových křivek mezi jednoduchými uzavřenými křivkami vzhledem ke každé ze čtyř studovaných faktorových pretopologií. . Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies.

English abstract

We discuss four quotient pretopologies of a certain basic topology on the digital plane. Three of them are even topologies and include the well-known Khalimsky and Marcus-Wyse topologies. Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies.

Keywords in Czech

Jordanovy křivky, topologie, faktorová pretopologie.

Keywords in English

Jordan curve, topology, quotient pretopology.

RIV year

2009

Released

21.09.2009

Publisher

Springer

ISSN

0302-9743

Journal

Lecture Notes in Computer Science (IF 0,513)

Volume

5810

Number

1

Pages from–to

252–262

Pages count

11

BIBTEX


@article{BUT49487,
  author="Josef {Šlapal},
  title="Jordan curve theorems with respect to certain pretopologies on Z^2",
  journal="Lecture Notes in Computer Science (IF 0,513)",
  year="2009",
  volume="5810",
  number="1",
  month="September",
  pages="252--262",
  publisher="Springer",
  issn="0302-9743"
}