PlanetMath: specialization

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specialization

(Definition)

Let be a topological space and suppose that $x\in X$ . Any point $y\in \overline{\{{x}\}}$ is called a specialization point of and we write $x\rightsquigarrow y$

For $Y\subset X$ the set

$\displaystyle \mathrm{Sp}(Y):=\{x\in X : \exists\, y\in Y\, y\in\overline{\{{x}\}} \}$

is called the specialization of

"specialization" is owned by jocaps.

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Keywords:

generization, specialization, generic points

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Cross-references: point, topological space
There are 2 references to this entry.

This is version 4 of specialization, born on 2006-11-04, modified 2006-11-04.
Object id is 8516, canonical name is Specialization.
Accessed 667 times total.

Classification:

AMS MSC:

54A05 (General topology :: Generalities :: Topological spaces and generalizations )

Pending Errata and Addenda

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