International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 425-428

A topology for automata II

Arun K. Srivastava1 and Wagish Shukla2

1Department of Mathematics, Banaras Hindu University, Varansi, India
2Department of Mathematics, Indian Institute of Technology, New Delhi, India

Received 6 October 1983

Copyright © 1986 Arun K. Srivastava and Wagish Shukla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A topology on the state set of an automaton is considered and it is shown that under this topology, genetically closed subsets and primaries, in the sense of Bavel [1] turn out to be precisely the regular closed subsets and minimal regular closed subsets respectively. The concept of a compact automaton is introduced and it is indicated that it can be viewed as a generalization of a finite automaton. Included also is an observation showing that our topological considerations can help recover some of the results of Dörfler [2].