A Pedagogical History of Compactness
Manya Raman-Sundström · American Mathematical Monthly · 2015
This paper traces the history of compactness from the original motivating questions through the development of the definition to a characterization of compactness in terms of nets and filters. The goal of the article is to clarify the central concepts of open-cover and sequential compactness, including details that a standard textbook treatment tends to leave out.