Topology: reference for "Great Wheel of Compactness"

This seems to be a very informative diagram showing the relationship between four forms of compactness in a general topological space. Prior to finding this I was trying to make sense of a seemingly countless (now seen to be countable = 12) collection of theorems relating one to another. The 12 relations are seen to simply to 6 proofs (A - F) and 6 corollaries by transitivity.

I found a version of this here https://pantherfile.uwm.edu/ancel/www/OLD%20COURSES/MATH%20752%20SPRING%202011/CHAPTER%20III/751.F10.IIIB-C.pdf

I haven't seen it anywhere else and would be interested if anyone has information about it.

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Solution 1:

From: Fredric D Ancel

Sent: 02 January 2016 22:08 To: Tom Collinge Subject: Re: Your (?) notes

Tom,

The diagram is a suped-up modification of one that I created sometime in the 1980’s for a Moore-method introductory graduate level topology I was teaching at University of Wisconsin-Milwaukee (or possible at the University of Oklahoma). It was in my notes for the class. The goal of the diagram was to help students keep track of the relations between various forms of compactness. Some students memorized it and would quote it back to me when I couldn’t remember these relations myself. The “great wheel” terminology is a humorous and probably politically incorrect reference to a Buddhist construct I read about is some Kipling novel.

The original diagram was created in a primitive version of Word (or possibly MacPaint) - no curved lines and very basic typography. Someone else has improved its aesthetics in the interim. I have attached an early version of the diagram below.