Questions tagged [topology]

Questions involving topology, the mathematical study of properties of spaces preserved by continuous maps.

8 questions with no upvoted or accepted answers
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Who discovered the singular cup product?

Cohomology is a stronger invariant than homology because it can be equipped with a ring structure. To be precise, if one starts with the singular cohomology groups $H^\bullet(-; R)$ with coefficients ...
3
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80 views

History of Braids

I am looking for papers or books that describe the history of the development of braid theory, mainly during the 19th and the 20th century. I know Moritz Epple book on the history of the theory of ...
2
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0answers
116 views

Several questions about Gauss's mathematical conception of braids

I'm trying to figure out several things about Gauss's thoughts concerning a certain four-strand braid. The reference my questions are based on is mainly Moritz Epple's excellent article "orbits of ...
2
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0answers
170 views

Set Theory, onto and into their relation to spoken language definitions

Does anyone know how the definitions for onto and into map to the spoken language definitions of the words? I compared the Bourbaki definitions to these words and have a suspicion that the German ...
2
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0answers
150 views

Why is the space of sections of $E$ called $\Gamma(E)$?

The space of sections of a bundle $\pi: E \to B$ is commonly denoted $\Gamma(E)$. (Note that the graph of a function $f$ is $\Gamma(f):=\left\{(x,f(x))\right\}$, and a particular section $\sigma: B \...
1
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96 views

Were the ancient Greeks aware of the “topology” of (Euclidean) space?

Related to a more mathematically inclined question, I'd like to ask the following question: The ancient Greeks made use of infinite arguments and processes (limits), e.g. in the method of exhaustion ...
0
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0answers
97 views

What if Newton's bucket had been a sphere?

My question is about Newton's bucket experiment. If a sphere filled (say) one-third with water is rotated very very fast, will the water eventually spread out across and coat the entire interior ...
0
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79 views

Riemann surfaces and covering

Assuming we have a Riemann surface $S$ of degree $n$ and we look at it as a covering of the projective line $\mathbb{P}^1$. If $B$ is the set of branch points of $S$ (when $B$ is a subset in $\mathbb{...