Okolí a konvergence vzhledem k uzávěrovému operátoru

Neighborhoods and convergence with respect to a closure operator

článek v časopise - ostatní, Jost

en

We study neighborhoods with respect to a categorical closure operator. In particular, we discuss separation and compactness obtained from neighborhoods in a natural way and compare them with the usual closure separation and closure compactness. We also introduce a concept of convergence based on using centered systems of subobjects, which naturally generalizes the classical filter convergence in topological spaces. We investigate behavior of the convergence introduced and show, among others, that it relates to the separation and compactness in natural ways.

Jsou studována okolí a konvergence vzhledem ke kategoriálnímu uzávěrovému operátoru. Zejména je diskutovány saparace a kompaktnost získané pomocí okolí obvyklým způsobem, které jsou porovnány s obvyklou separací a kompaktností. Je také zaveden a studován pojem konvergence založený na využití centrovaných systémů podobjektů, která přirozeným způsobem zobecňuje topologockou konvergenci využívající filtrů . also introduce a concept of convergence based on using centered

We study neighborhoods with respect to a categorical closure operator. In particular, we discuss separation and compactness obtained from neighborhoods in a natural way and compare them with the usual closure separation and closure compactness. We also introduce a concept of convergence based on using centered systems of subobjects, which naturally generalizes the classical filter convergence in topological spaces. We investigate behavior of the convergence introduced and show, among others, that it relates to the separation and compactness in natural ways.

Okolí, konvergence, uzávěrový operátor

Neighborhoods, convergence, closure operator

2011

25.08.2011

0139-9918

Mathematica Slovaca

61

5

717–732

16