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8

Cohn himself recommends historical notes at the end of sections 15, 16 of Abstract Harmonic Analysis by Hewitt and Ross, volume 1. Here is an excerpt: "Invariant integration on one or another special class of groups has long been known and used. A detailed computation of the invariant integral on $\mathfrak{SD}(n)$ was given in 1897 by HURWITZ [1]. ...


4

Try these references: Section 7.5 of History of Topology, edited by I. M. James. Section 2.2 of the chapter "Topological Features of Topological Groups" in Handbook of the History of General Topology, volume 3, edited by C.E. All and R. Lowen


4

Here is a partial answer. By the time these definitions were introduced as definitions there was a body of previous work, where they were convenient side notions for stating theorems in special cases for subsets of real line, plane, and then curve and function spaces (Cantor's accumulation points, derived and closed sets on the line, Weierstrass's theorems, ...


4

I don't entirely understand the question, but this book is probably relevant: J. H. Manheim, The Genesis of Point Set Topology (1964). I must have borrowed it from a library a long time ago. It is out of print. Used copies go for about a hundred quid. I suppose Dover might look kindly on a request for a reprint. This is very probably also relevant (and it ...


4

I. M. James, History of Topology. This is a collection of 40 essays by different authors, on topics related mostly to manifolds and algebraic topology. Perhaps the page http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Topology_in_mathematics.html will be of interest for aspects of topology before Poincaré came on the scene.


3

J. Dieudonne, A History of Algebraic and Differential Topology, 1900 - 1960.


2

Definition through interior points can be obtained by its dual version first proposed by Kuratowski in 1922, which is known as Kuratowski Closure Algebra. Historically, definition through closure points (Closure Algebra) came first and the one by interior points followed after it. The following three versions for the definition of topological spaces are ...


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