Math and science::Topology
Closed subsets
Closed subsets, definition
Let
The below properties of closed sets can be derived.
Lemma. [hidden as it gives away the below cloze.]
Let
- Whenever
and are closed subsets of , then [...] is also closed in X. - Whenever
is a family (finite or not) of closed subsets of , then [...] is closed in . - [something] and [something] are closed subsets of
.
This lemma follows from the application of de Morgan's laws to the definition of a topological space.