Questions tagged [topology]

Question 1

In Bourbaki's General Topology, 1995, on Ch. I, §9.1, in Definition I, a space $X$ is defined to be quasi-compact if it satisfies the condition: (C''') Every open cover has a finite subcover. and in ...

Question 2

I want books in real analysis, topology and abstract algebra that provide the intuition and history behind each definition, theorem and proof. I want to know about the historical development of modern ...

Question 3

I have found a paper with a topological proof of the Fundamental Theorem of Arithmetic (published in The Mathematics Student by the Indian Mathematical Society, Vol. 93, Part 3-4, 2024). You can find ...

Question 4

(The following query by Noam Zeilberger has recently appeared on the Categories mailing list; I am taking the liberty of asking it here.) In Ulam's autobiography Adventures of a Mathematician, there ...

Question 5

I would like to clarify a couple points in the following excerpt from these notes (page 3) discussing Grothendieck's seminal Esquisse d’un programme pointing out the importance to reformalize the ...

Question 6

I read a book "a history of abstract algebra"- chapter 6 by Israel Kleiner. And in this book, it is said that Emmy Noether gave a presentation at the ICM congress held in Zurich in 1932, ...

Question 7

I read 17 equations that changed the world by Ian Stewart. This book provides information about the correlation between electromagnetic force and topological invariant. The idea of a topological ...

Question 8

Nowadays the unique 2 point, nondiscrete, nontrivial topological space goes by the name of the Sierpinski space. How did that space come to be named after Sierpinski? The comments to this MathOverflow ...

Question 9

Among the many cohomology theory's branches I asked about last time, I was curious about $d^2=0$ because I know that it is the formula that is the basis of all cohomology. So this time, I would like ...

Question 10

I saw this post. And I already posted it on Math stack exchange, but since someone recommended this site, I'm refining it and posting it again. And I understand that the mathematical object called ...

Question 11

In Moritz Epple's article "Geometric Aspects in the Development of Knot Theory", Epple writes the following: It has been suggested that one of the earliest tools of combinatorial knot ...

Question 12

Since I've not gotten any answers after a bit more than a week, I've now cross-posted to MathOverFlow. EDIT 2023-08-15: Several commenters here and at MO have asked me to sharpen the original question....

Question 13

How and when did the dedicated study of locally compact groups begin? Specific instances from literature, recorded stories, etc., may help supplement the answers. There seems to be no reason why I ...

Question 14

Bachelors' unknotting is a way to show that all tame knots are isotopic to the unknot, by tightening a knot to a point. Why is it called 'bachelors' unknotting'?

Question 15

Is the idea of a continuous map in the point-set model of topological spaces, i.e. that the preimages of opens are open, due to Hausdorff (Grundzüge der Mengenlehre)? For example, does the notion of ...

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Questions tagged [topology]

Origin of quasi-compactness

Can you suggest textbook for history of modern mathematics like topology and abstract algebra?

A topological proof of the fundamental theorem of arithmetic

Did Ulam discover category theory?

Grothendieck's Fine Topology in Esquisse d’un programme

Emmy Noether's announcement in 1932 ICM

Relationship between electromagnetic and topological invariant

Origin of "Sierpinski space"?

Motivation and history of singular homology

History of cohomology theory

Was the "Gauss word realization problem" a kind of unknotting problem?

Early illustrations of topological notions in published work

How and when did the dedicated study of locally compact groups begin?

Why is bachelors' unknotting called as such and who discovered it?

Continuity, Hausdorff

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