Further properties of nano pre-$T_0$, nano pre-$T_1$ and nano pre-$T_2$ spaces

Further properties of nano pre-$T_0$, nano pre-$T_1$ and nano pre-$T_2$ spaces

**Authors : **

P. Sathishmohan^{1} , V. Rajendran^{ 2} and P.K. Dhanasekaran^{ 3}

**Author Address : **

^{1,2} Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, Tamil Nadu,India.

^{3 }Research Scholar, Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, Tamil Nadu,India.

*Corresponding author.

**Abstract : **

The basic objective of this paper is to define nano-$T_0$ space, nano semi-$T_0$ space, nano pre-$T_0$ space, nano-$T_1$ space, nano semi-$T_1$ space, nano pre-$T_1$ space, nano-$T_2$ space, nano semi-$T_2$ space and nano pre-$T_2$ space and investigate their properties. Also we have obtain some of their basic results and given an appropriate examples to understand the abstract concepts clearly.

**Keywords : **

Nano-$T_0$ space, nano semi-$T_0$ space, nano pre-$T_0$ space, nano-$T_1$ space, nano semi-$T_1$ space, nano pre-$T_1$ space, nano-$T_2$ space, nano semi-$T_2$ space and nano pre-$T_2$ space.

**DOI : **

**Article Info : **

*Received : * July 21, 2018; *Accepted : * December 22, 2018.