On the number of topologies definable for a finite set
- 1 May 1968
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 8 (2) , 194-198
- https://doi.org/10.1017/s1446788700005231
Abstract
No general rule for determining the number N(n) of topologies definable for a finite set of cardinal n is known. In this note we relate N(n) to a function Ft(r1,…, rt+1) defined below which has a simple combinatorial interpretation. This relationship seems useful for the study of N (n). In particular this can be used to calculate N(n) for small values. For n 3, 4, 5, 6 we find N(3) = 29, N(4) = 355, N(5) = 7,181, N(6) = 145,807.Keywords
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