Editing Empty set (section)

=== Topology ===
In any [[topological space]] <math>X</math>, the empty set is [[open set|open]] by definition, as is <math>X</math>. Since the [[Complement (set theory)|complement]] of an open set is [[Closed set|closed]] and the empty set and <math>X</math> are complements of each other, the empty set is also closed, making it a [[clopen set]]. Moreover, the empty set is [[Compact set|compact]] by the fact that every [[finite set]] is compact.

A topological space <math>X</math> is said to have the [[indiscrete topology]] if the only open sets are <math>\varnothing</math> and the entire space.

The [[Closure (mathematics)|closure]] of the empty set is empty. This is known as "preservation of [[nullary]] [[Union (set theory)|unions]]".<ref>{{cite book |last1=Munkres |first1=James Raymond |title=Topology |date=2018 |publisher=Pearson |location=New York, NY |isbn=978-0134689517 |edition=Second, reissue}}</ref>