Difference between revisions of "Tightness of a topological space"
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| − | One of the [[cardinal characteristic]]s of a [[topological space]] $X$. The ''local tightness'' $t(x,X)$ at a point $x \in X$ is the least cardinality $\mathfrak{t}\ge\ | + | One of the [[cardinal characteristic]]s of a [[topological space]] $X$. The ''local tightness'' $t(x,X)$ at a point $x \in X$ is the least cardinality $\mathfrak{t}\ge\aleph_0$ such that if $x$ is in the closure $\bar A$, then $A$ contains a subset $B$ of cardinality $\le \mathfrak{t}$ with $x \in\bar B$ . The tightness $t(X)$ is the least upper bound of the local tightness. |
====References==== | ====References==== | ||
* Mary Ellen Rudin, ''Lectures on Set Theoretic Topology'', American Mathematical Society (1975) ISBN 0-8218-1673-X {{ZBL|0318.54001}} | * Mary Ellen Rudin, ''Lectures on Set Theoretic Topology'', American Mathematical Society (1975) ISBN 0-8218-1673-X {{ZBL|0318.54001}} | ||
Revision as of 20:21, 3 January 2018
2020 Mathematics Subject Classification: Primary: 54A25 [MSN][ZBL]
One of the cardinal characteristics of a topological space $X$. The local tightness $t(x,X)$ at a point $x \in X$ is the least cardinality $\mathfrak{t}\ge\aleph_0$ such that if $x$ is in the closure $\bar A$, then $A$ contains a subset $B$ of cardinality $\le \mathfrak{t}$ with $x \in\bar B$ . The tightness $t(X)$ is the least upper bound of the local tightness.
References
- Mary Ellen Rudin, Lectures on Set Theoretic Topology, American Mathematical Society (1975) ISBN 0-8218-1673-X Zbl 0318.54001
How to Cite This Entry:
Tightness of a topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tightness_of_a_topological_space&oldid=42686
Tightness of a topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tightness_of_a_topological_space&oldid=42686