Seperation Axioms in Micro Semi Pre-Topological Spaces

The primary objetive of this paper is to introduce a new type of separation axioms namely, micro semi pre-T0, micro semi pre-T1, micro semi pre-T2 and to obtain their properties. Also, the relationship between these spaces with related concepts are investigated. Introduction: In 2019, S. Chandrasekar [3] introduction of micro topology as a straightforward expansion from nano topology, emphasizing micro pre-open and micro semi-open sets. H.Z. Ibrahim [6] introduced micro β-open sets in micro topological spaces. In 2020, Hariwan Z. Ibrahim [7] introduced the separation axioms on micro topology with particular focus on micro-open sets. In this paper some new types of spaces are define and study in micro topological spaces namely, micro semi pre T0, micro semi pre T1, micro semi pre T2, using the concept of micro semi pre open sets. Also, the properties of these spaces and the relationship between these spaces with related concepts are found. Conclusions: In this paper introduces and investigates new types of micro semi pre topological spaces, namely micro semi pre T0, micro semi pre T1, and micro semi pre T2, extending concepts from previous works on micro topology. The properties and relationships of these spaces are explored, shedding light on their separation axioms and connections with related concepts like micro-T0, micro-T1, and micro-T2 spaces. The study presented here not only expands the theoretical framework of micro topology but also provides insights into the interplay between different types of micro topological spaces. Overall, this paper contributes to the ongoing development of micro topology by introducing and analyzing micro semi pre topological spaces, leading the way for further research in this area and potentially finding applications in various mathematical and scientific disciplines. In Future, connecting separation axioms in topology to the behavior of an RLC circuit within micro topology provides a rigorous mathematical framework to distinguish and analyze different states and transitions. This approach not only enhances our understanding of the circuit’s dynamics but also offers a robust method to explore micro particle interactions and configurations within a topological space.