On the Computer Enumeration of Finite Topologies The problem of enumerating the number of topologies which can be formed from a finite point set is considered both theoretically and computationally. Certain fundamental results are established, leading to an algorithm for enumerating finite topologies, and computed results are given for n <= 7. An interesting side result of the computational work was the unearthing of a theoretical error which had been induced into the literature; the use of the computer in combinatorics represents, chronologically, an early application, and this side result underscores its continuing usefulness in this area. CACM May, 1967 Evans, J. W. Harary, F. Lynn, M. S. CA670507 JB February 28, 1978 10:37 AM 1595 5 1595 1595 5 1595 1595 5 1595