The Development of Topology Based Open Sets, Closed Sets, and Limit Points: An Analytical Study

The Evolution of Topology and its Fundamental Concepts

Abstract

General topology has its basic establishments in real and complex investigation, which made critical vocations of the interrelated thoughts of open set, of closed set, and of a limit motivation behind a set. This article inspects how those three ideas developed and advanced during the late nineteenth and mid twentieth hundreds of years, because of Weierstrass, Cantor, and Lebesgue. Specific consideration is paid to the various types of the Bolzano–Weierstrass Theorem found in the last's unpublished talks. A fruitless early, unpublished introduction of open sets by Dedekind is inspected, just as how Peano and Jordan nearly presented that idea.