Topology

S.Archana; P.Elavarasi

doi:https://doi.org/10.14445/22315373/IJMTT-V62P525

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 62 | Number 3 | Year 2018 | Article Id. IJMTT-V62P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V62P525

Topology

S.Archana, P.Elavarasi

Citation :

S.Archana, P.Elavarasi, "Topology," International Journal of Mathematics Trends and Technology (IJMTT), vol. 62, no. 3, pp. 178-183, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V62P525

Abstract

In this project we are going to explore the “Countable Topological Spaces” in greater details. We shall try to understand how these axioms are affected to spaces, by taking open and closed sets. A clear idea of the separation properties typical of the spaces we are studying helps us understand what kind of proof techniques to use. When working with T1- Spaces, we use that points are closed. In particular, the inverse image of (via a continuous function) of a points in a T1- Spaces is a closed sets. Finally we conclude that an Axiom of Countability is a properties of certain mathematical objects that requires the existence of a countable set with certain properties, while without it such sets might not exists.

Keywords

Countable spaces, T1 – spaces, Regular spaces

References

[1] J.L.Kelly, General topology, Dover Edition, Van Nostrand, Reinhold co., New York.
[2] George F. Simmons, Introduction to topology and Modern Analysis, Third Edition McGraw Hill Book co.1963.
[3] James R Munkres, Introduction to topology, Second Edition, 2000.
[4] L.Steen and J. Seeback, counter examples in topology, Second Edition Holt, Rinehart and Winston, New York, 1970.
[5] P.Veeramani, General Topology, Indian Institute of Technology Madras.