Category:Closure Operators

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This category contains results about Closure Operators in the context of Mapping Theory.
Definitions specific to this category can be found in Definitions/Closure Operators.


Let $\struct {S, \preceq}$ be an ordered set.


A closure operator on $S$ is a mapping:

$\cl: S \to S$

which satisfies the following conditions for all elements $x, y \in S$:

$\cl$ is inflationary       \(\ds x \)   \(\ds \preceq \)   \(\ds \map \cl x \)             
$\cl$ is increasing       \(\ds x \preceq y \)   \(\ds \implies \)   \(\ds \map \cl x \preceq \map \cl y \)             
$\cl$ is idempotent       \(\ds \map \cl {\map \cl x} \)   \(\ds = \)   \(\ds \map \cl x \)             

Subcategories

This category has the following 9 subcategories, out of 9 total.

Pages in category "Closure Operators"

The following 29 pages are in this category, out of 29 total.