# Spread

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 54A25 [MSN][ZBL]

One of the cardinal characteristics of a topological space $X$. The least upper bound of the cardinalities of discrete subspaces of $X$.

For a Hausdorff space $X$, the spread is related to the density $d(X)$ and cardinality $|X|$ by results of Hajnal and Juhász: $$ d(X) \le 2^{s(X)} \, ; $$ $$ |X| \le 2^{2^{s(X)}} \ . $$

#### References

- Mary Ellen Rudin,
*Lectures on Set Theoretic Topology*, American Mathematical Society (1975) ISBN 0-8218-1673-X Zbl 0318.54001 - András Hajnal; István Juhász "Some results in set-theoretic topology"
*Sov. Math., Dokl.***8**(1967) 141-143 Zbl 0153.52102 - András Hajnal; István Juhász "Discrete subspaces of topological spaces"
*Nederl. Akad. Wet., Proc., Ser. A***70**(1967) 343-356 Zbl 0163.17204

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Spread.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Spread&oldid=42659