What is the history of the modern definition of a topological space?

Peter Scholze has said that the toughest thing is to get the definitions right, and this is certainly on of mathematics’ most important.

This definition (and how it can connect to more intuitive notions of continuity and topology) certainly wasn’t created overnight. Are there any resources where I can read about its history? As in, how mathematics came to accept this weird set of conditions as capturing the notion of a topological space?

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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs https://nevinmanimala.com

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