Tightness of a topological space

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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.


  • Mary Ellen Rudin, Lectures on Set Theoretic Topology, American Mathematical Society (1975) ISBN 0-8218-1673-X Zbl 0318.54001
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