Question

prove that the union of two closed set is a closed sets​

Answer 1

Step-by-step explanation:

Let X be a sample space. If F⊂X is closed for 1≤i≤n, prove that ⋃ni=1Fi is also closed. Note that the theorem is not necessarily true for an infinite collection of closed {Fα}.

Here are the definitions I'm using:

Let X be a metric space with distance function d(p,q). For any p∈X, the neighborhood Nr(p) is the set {x∈X|d(p,x)<r}. Any p∈X is a limit point of E if ∀r>0, Nr(p)∩E≠{p} and ≠∅. Any subset E of X is closed if it contains all of its limit points.

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