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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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