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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 specialization point of $ x$ 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 $ Y$.



"specialization" is owned by jocaps.
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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
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 MSC54A05 (General topology :: Generalities :: Topological spaces and generalizations )

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