A study on (c, d) IF − Q uniform spectral spaces

Abstract

A conceptual way of approach to sober space is explored by the irreducibility of closed sets and their components in topological spaces. Sober space has been defined by both generic points and the irreducibility of closed sets. From this, the extension of a novel space which is known as spectral space is developed. Spectral space is one of the inventive extensions of sober space. Spectral space, can also be studied along with compact spaces, T0 space and sober space in topological space. T0 space has played a major role in spectral space. Quasi-spectral space and Semi-spectral space are also probed in addition to spectral space. In this article, the author introduces a new concept called (c, d) IF − Q uniform irreducible closed set. By using it the new space called (c, d) IF − Q uniform sober space is introduced and studied. The extension of (c, d) IF – Q uniform sober space is studied as (c, d) IF − Q uniform spectral space. Moreover, (c, d) IF − Q uniform semi-spectral space and (c, d) IF − Q uniform quasi-spectral space are also introduced and some of its properties are discussed.