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Math and science::Topology

Closed subsets

Closed subsets, definition

Let X=(X,T) be a topological space. A subset VX is closed iff [...].

The below properties of closed sets can be derived.

Lemma. [hidden as it gives away the below cloze.]

Let X=(X,T) be a topological space. Then

  1. Whenever V1 and V2 are closed subsets of X, then [...] is also closed in X.
  2. Whenever (Vi)iI is a family (finite or not) of closed subsets of X, then [...] is closed in X.
  3. [something] and [something] are closed subsets of X.

This lemma follows from the application of de Morgan's laws to the definition of a topological space.