Cover (mathematics) | Wikipedia audio article

Описание: This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Cover_(...)


00:00:35 1 Cover in topology
00:01:10 2 Refinement
00:02:03 3 Subcover
00:02:56 4 Compactness
00:03:31 5 Covering dimension
00:04:06 6 See also



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SUMMARY
=======
In mathematics, a cover of a set



X


{\displaystyle X}
is a collection of sets whose union contains



X


{\displaystyle X}
as a subset. Formally, if




C
=
{

U

α


:
α
∈
A
}


{\displaystyle C=\lbrace U_{\alpha }:\alpha \in A\rbrace }
is an indexed family of sets




U

α




{\displaystyle U_{\alpha }}
, then



C


{\displaystyle C}
is a cover of



X


{\displaystyle X}
if




X
⊆

⋃

α
∈
A



U

α


.


{\displaystyle X\subseteq \bigcup _{\alpha \in A}U_{\alpha }.}