Publication detail

A digital pretopology and one of its quotients

ŠLAPAL, J.

Czech title

A digital pretopology and one of its quotients

English title

A digital pretopology and one of its quotients

Type

journal article - other

Language

en

Original abstract

We introduce a certain pretopology on the digital plane $\mathbb Z^2$ and present a digital analogue of the Jordan curve theorem for for it. We then discuss a topology on $\mathbb Z^2$ which is shown to be a quotient pretopology of the pretopology introduced. This fact is used to prove a digital Jordan curve theorem also for this topology.

Czech abstract

We introduce a certain pretopology on the digital plane $\mathbb Z^2$ and present a digital analogue of the Jordan curve theorem for for it. We then discuss a topology on $\mathbb Z^2$ which is shown to be a quotient pretopology of the pretopology introduced. This fact is used to prove a digital Jordan curve theorem also for this topology.

English abstract

We introduce a certain pretopology on the digital plane $\mathbb Z^2$ and present a digital analogue of the Jordan curve theorem for for it. We then discuss a topology on $\mathbb Z^2$ which is shown to be a quotient pretopology of the pretopology introduced. This fact is used to prove a digital Jordan curve theorem also for this topology.

Keywords in Czech

Pretopology, quotient pretopology, digital plane, Jordan curve

Keywords in English

Pretopology, quotient pretopology, digital plane, Jordan curve

RIV year

2012

Released

01.01.2012

ISSN

0146-4124

Volume

39

Number

2

Pages from–to

13–25

Pages count

13

BIBTEX


@article{BUT50374,
  author="Josef {Šlapal},
  title="A digital pretopology and one of its quotients",
  year="2012",
  volume="39",
  number="2",
  month="January",
  pages="13--25",
  issn="0146-4124"
}