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specialization (Definition)

Let $X$ be a topological space and suppose that $x\in X$ Any point $y\in \overline{\{{x}\}}$ is called a <</SPAN>#44#>specialization point of $x$ and we write $x\rightsquigarrow y$

For $Y\subset X$ the set $$\mathrm{Sp}(Y):=\{x\in X : \exists\, y\in Y\, y\in\overline{\{{x}\}} \}$$ is called the specialization of $Y$




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See Also: partial ordering in a topological space

Keywords:  generization, specialization, generic points
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Cross-references: point, topological space
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This is version 4 of specialization, born on 2006-11-04, modified 2006-11-04.
Object id is 8516, canonical name is Specialization.
Accessed 1141 times total.

Classification:
AMS MSC54A05 (General topology :: Generalities :: Topological spaces and generalizations )

Pending Errata and Addenda
1. Please add more content.. by CWoo on 2009-03-23 18:59:43
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