Spread

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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 Template:ZBL
• András Hajnal; István Juhász "Some results in set-theoretic topology" Sov. Math., Dokl. 8 (1967) 141-143 Template:ZBL
• András Hajnal; István Juhász "Discrete subspaces of topological spaces" Nederl. Akad. Wet., Proc., Ser. A 70 (1967) 343-356 Template:ZBL