IJPAM: Volume 118, No. 1 (2018)

Title

TOPOLOGIES ON FINITE SETS

Authors

Narendrakumar R. Dasre$^1$, Pritam R. Gujarathi$^2$
$^{1,2}$Department of Engineering Sciences
Ramrao Adik Institute of Technology
Nerul, Navi Mumbai-400706, INDIA

Abstract

In this paper, we have computed the repeated ratios of number of topologies on finite sets with the reference to the series A000798 [1]. The bound for number of topologies on finite sets is determined by many people [2,3]. We have also obtained the sharper bounds for the number of topologies on the set with n elements.

History

Received: 2017-04-18
Revised: 2017-08-19
Published: February 15, 2018

AMS Classification, Key Words

AMS Subject Classification: 40A15, 54A99
Key Words and Phrases: topology, repeated ratio, lower bound, upper bound, sequence

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Bibliography

1
N.J.A. Sloane, Online Encyclopedia of Integer Sequences, at http://oeis.org/A000798/list

2
G.H. Patil and M.S. Chaudhary, A recursive determination of topologies on finite sets, Indian Journal of Pure and Applied Mathematics, 26, No. 2 (1995), 143-148.

3
V. Kishnamurthy, On the number of topologies on a finite set, The American Mathematical Monthly, 73, No. 2 (1966), 154-157.

How to Cite?

DOI: 10.12732/ijpam.v118i1.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 118
Issue: 1
Pages: 39 - 48


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