Spread

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