A unified theory of perfect and related functions

Authors

  • M. N. Mukherjee Depat. of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, Calcutta – 700019, India Author
  • S. Raychaudhuri Depat. of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, Calcutta – 700019, India Author

Keywords:

$\beta$-perfect function, operator $\alpha$, $\beta$-set, $\gamma$-set, $\beta$-closed function, $\beta$-convergence and $\beta$-adherence of filter-bases

Subjects:

54C10

Abstract

A unified theory has been developed on the basis of the similarity in properties of perfect and allied types of functions. The theory intromites as a starting point a certain subset of $\Cal P(X)$, the power set of a nonvoid set $X$, and an operator $\alpha$ on $\Cal P(X)$; a second operator $\beta$ is also brought into action. This theory of $\beta$-perfect functions includes the theories of perfect, $\theta$-perfect and $\delta$-perfect functions and is seen to generate many new types of functions when different pairs of operators take the roles of the pair $(\alpha,\beta)$.

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Published

1993-10-15

Issue

Vol. 45 No. 1–4 (1993): Vol. 45, Issue 1–4

Section

Articles

License

Copyright (c) 1993 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.