Structural Presentation of Some Concepts in Metric Spaces and Topological Spaces

Volume 8, Issue 2, April 2023     |     PP. 19-28      |     PDF (1236 K)    |     Pub. Date: August 1, 2023
DOI: 10.54647/dee470327    97 Downloads     243534 Views  

Author(s)

Pandit U. Chopade, Department of Mathematics, Dnyanopasak Shikshan Mandal’s Arts, Commerce and Science College, Jintur, Dist. Parbhani (MS)

Abstract
The concept of metric space and topological space grew out of the study of real line and Euclidean space and study of continuous function on these spaces. In this Paper, we will try to discuss some concepts in metric spaces and topological spaces whose meanings are same but presented by the different ways. We will discuss open sets, closed sets, continuity and connectedness in the reference to metric space and topological space.

Keywords
Metric Space, Topological Space and Compactness

Cite this paper
Pandit U. Chopade, Structural Presentation of Some Concepts in Metric Spaces and Topological Spaces , SCIREA Journal of Electrical Engineering. Volume 8, Issue 2, April 2023 | PP. 19-28. 10.54647/dee470327

References

[ 1 ] Richard R. Goldberg, Methods of Real Analysis, Oxford & IBH Publishing Co. Pvt. Ltd., New Delhi.
[ 2 ] R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis, John Wiley & Sons (Asia) P. Ltd, 2002.
[ 3 ] William F. Trench, Introduction to Real Analysis, Pearson Education Pub.
[ 4 ] T. M. Apostol, Calculus (Vol.1), John Wiley & Sons (Asia) P. Ltd., 2002.
[ 5 ] K. A. Ross, Elementary Analysis-The Theory of Calculus Series-Undergraduate Text in Mathematics, Springer Verlag, 2003.
[ 6 ] James R. Munkres, Topology, Second Edition, Pearson Education P. Ltd. India, 2000.
[ 7 ] Maynard J. Mansfield, Introduction to topology.
[ 8 ] S. C. Malik and Savita Arora, Mathematical Analysis, New Age International (P) Limited, Publishers.