An approach to change the topology of a topological space with the help of its closed sets in the presence of grills

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

The aim of this paper is introduce an approach to convert the
topology of a topological space to another topology(in fact, a coarser topology).
For this purpose, considering a closed set P of subsets of a topological space
(X; T) and a grill G on the space, we use the closure operator cl associated with
T, to define a new Kuratowski closure operator cl_p
on X. The operator cl_p
induces the desired topology. We then characterize the form of this resulting
topology and also determine its relationship to the initial topology of the space.
Some examples are given. Also, using a suitable grill in the method, we convert
each topological space to corresponding D-space.

Keywords

References

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Journal of Mahani Mathematical Research
Volume 10, Issue 2
Special Issue Dedicated to Professor M. Radjabalipour on the occasion of his 75th birthday.
October 2021
Pages 9-19

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History

  • Receive Date: 25 January 2021
  • Revise Date: 16 February 2021
  • Accept Date: 11 April 2021

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