A digital pretopology and one of its quotients

A digital pretopology and one of its quotients

A digital pretopology and one of its quotients

článek v časopise

en

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.

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.

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.

Pretopology, quotient pretopology, digital plane, Jordan curve

2012

01.01.2012

13

25

13