Micro Pre Separation Axioms in Circuit of Light System on Four Stroke Engines

The basic objective of this research work is to introduce and investigate the properties of micro-T0, T1, T2 spaces, micro semi-T0, T1, T2 and micro pre- T0, T1, T2 spaces using the concept of micro open, micro semi-open and micro pre-open sets and comparing them to the circuit system of light in four stroke engines. Introduction: Levine’s introduction of generalized closed sets in 1970 [7], providing a foundational framework for subsequent developments. In 1975, Maheshwari and Prasad [9] gave the idea about the s-normal spaces and in 1990, Ashish Kar and Bhattacharyya [1] introduced the concept of weak separation axioms. In 1995, Chattpadhyay [3] investigated some properties of pre-T0, pre-T1 and pre-T2 spaces in topological spaces. In 2013, Lellis Thivagar [6] defined the new concept of Nano topology based on generalized closed sets. In 2019, Sathishmohan et al., [10] established the concepts of nano pre-T0, nano pre-T1 and nano pre-T2 spaces and obtain many interesting results. In 2019, Chandrasekar [2] introduced the concept of Micro topology which is a simple extension of nano topology with focus on micro pre-open and micro semi-open sets. In 2020, Hariwan Z. Ibrahim [4] introduced the separation axioms on micro topology with particular focus on micro open sets. In 2022, Wei Liu et al., [12] established the importance of battery in electric vehicles and at 2024, Liu. H et al., [8] studied the control of angle formation based on circuit diagrams. This motivates us to introduce and study some new concepts of micro-T0, T1, T2 spaces, micro semi-T0, T1, T2 spaces and micro pre- T0, T1, T2 spaces combining with the circuit of the four stroke engines. Conclusions: In this paper, we introduced the notions of micro semi-T0, T1, T2 and micro pre-T0, T1, T2 by employing the concepts of separation axioms elucidating various associated properties. Based on the theorems and results, I have concluded that circuit of the light system in vehicles and the study of my spaces are more closely related to each other. Our intent is to further elaborate on those findings in forthcoming research endeavors, with a particular focus on exploring practical applications.