**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Preclosure operator

Summary

In topology, a preclosure operator or Čech closure operator is a map between subsets of a set, similar to a topological closure operator, except that it is not required to be idempotent. That is, a preclosure operator obeys only three of the four Kuratowski closure axioms.
Definition
A preclosure operator on a set X is a map [\ \ ]_p
:[\ \ ]_p:\mathcal{P}(X) \to \mathcal{P}(X)
where \mathcal{P}(X) is the power set of X.
The preclosure operator has to satisfy the following properties:
# [\varnothing]_p = \varnothing ! (Preservation of nullary unions);

# A \subseteq [A]_p (Extensivity);

# [A \cup B]_p = [A]_p \cup [B]_p (Preservation of binary unions).

The last axiom implies the following:
: 4. A \subseteq B implies [A]_p \subseteq [B]_p.
Topology
A set A is closed (with respect to the preclosure) if [A]_p

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications

Related people

No results

No results

Related courses

No results

Related units

Related concepts

Related lectures

No results

No results

No results