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{{TEX|done}}{{MSC|54A25}}

One of the [[cardinal characteristic]]s 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 (of a topological space)|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}}