Introduction to D-Space & C- Space

Nikhitha P B

doi:https://doi.org/10.14445/22315373/IJMTT-V59P542

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 59 | Number 5 | Year 2018 | Article Id. IJMTT-V59P542 | DOI : https://doi.org/10.14445/22315373/IJMTT-V59P542

Introduction to D-Space & C- Space

Nikhitha P B

Abstract

To reference in my paper, at first, I would like a text of ‘Introduction to General Topology’that addressed convergence of a sequence in topological spaces. The concept seems plausible .Quite interested to consider the convergence of real sequence (1/n)with respect to different topology onreal spaceɌ . All of us knew that (1/n) converges to 0with respect to usual topology on Ɍ. Here I pursue my work on discussing the space on which (1/n) divergent and stronger than usual topology on Ɍ. In consideration of this I am trying to define a new concept of D- Space and C- Space.

Keywords

( Ɍ,𝜏1 ) : Indiscrete Topology

( Ɍ,𝜏2 ) : Discrete Topology

( Ɍ,𝜏3 ) : Co-FiniteTopology

( Ɍ,𝜏4 ) : Co-Countable Topology

( Ɍ,𝜏5 ) : Usual Topology

( Ɍ,𝜏6 ) : Upper-Limit Topology

( Ɍ,𝜏7 ) : Lower -Limit Topology

( Ɍ,𝜏8 ) : Scattering Topology

( Ɍ,𝜏9 ) : Ray Topology

∅ ∶ 𝑁𝑢𝑙𝑙 𝑆𝑒𝑡

∈ ∶ 𝐵𝑒𝑙𝑜𝑛𝑔𝑠𝑇𝑜

∀ ∶ 𝐹𝑜𝑟 𝐴𝑙𝑙

∃ ∶ 𝑇ℎ𝑒𝑟𝑒 𝐸𝑥𝑖𝑠𝑡𝑠

References

[1] K.D.Jhoshi , Introduction to General Topology, ISBN:978-0-85226-44-7

Citation :

Nikhitha P B, "Introduction to D-Space & C- Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 59, no. 5, pp. 300-303, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V59P542