Questions tagged [topology]
Questions involving topology, the mathematical study of properties of spaces preserved by continuous maps.
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Did Ulam discover category theory?
(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 ...
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Grothendieck's Fine Topology in Esquisse d’un programme
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 ...
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Emmy Noether's announcement in 1932 ICM
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, ...
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Relationship between electromagnetic and topological invariant
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 ...
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Origin of "Sierpinski space"?
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 ...
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Motivation and history of singular homology
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 ...
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History of cohomology theory
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 ...
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Was the "Gauss word realization problem" a kind of unknotting problem?
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 ...
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Why the sphere eversion problem emerged?
Sphere eversion is the process of turning a sphere inside out in a three-dimensional space. See also this animation on YouTube: Outside in (2011) and picture below. My question is, what is the ...
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Lefschetz historical proof of Hyperplane Theorem
I would like to understand the the idea behind the historically original proof by Lefschetz of his Hyperplane theorem sketched roughly Here. The basic setup:
Let $X$ be an $n$ -dimensional complex ...
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Early illustrations of topological notions in published work
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....
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How and when did the dedicated study of locally compact groups begin?
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 ...
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Why is bachelors' unknotting called as such and who discovered it?
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'?
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Continuity, Hausdorff
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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Topologies without the axiom that finite intersection of open sets is open
A topology is a pair of
a nonempty set $P$ of points, and
a set $Opens\subseteq 2^P$ of open sets that is closed under two closure conditions:
arbitrary (possibly infinite) unions and
finite (...
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