# Tightness of a topological space

From Encyclopedia of Mathematics

2010 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=42687