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3
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'Specialization'
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| Title of object: |
Specialization |
| Canonical Name: |
Specialization |
| Type: |
Definition |
| Created on: |
2006-11-04 06:32:42 |
| Modified on: |
2006-11-04 07:33:04 |
| Classification: |
msc:54A05 |
| Keywords: |
generization, specialization, generic points |
| Defines: |
specialization |
Revision comment (for changes between this and next version):
| Changes for correction #10807 ('defines'). |
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Content:
Let $X$ be a topological space and suppose that $x\in X$.
Any point $y\in \overline{\{{x}\}}$ is called a \emph{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 \emph{specialization of} $Y$. |
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