Questions involving topology, the mathematical study of properties of spaces preserved by continuous maps.
Questions tagged [topology]
69 questions
5
votes
1 answer
History of covering spaces
I want to know what lead to the notion of covering spaces, and the evolution of the concept. I understand that topology was not developed to solve problems, but to gain insight into the foundation of mathematics. So, what insight lead to the…
Avatrin
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4
votes
1 answer
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 fibers of a ring morphism predate the said book…
Hypatia du Bois-Marie
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4
votes
3 answers
The First Published book on Algebraic Topology
As far as I know, according to google, Eilenberg, Steenrod's book: Foundations of Algebraic Topology was published in 1952, and Spanier's book: Algebraic Topology was published in 1966.
My Questions are the following:
Is there any book on…
Saikat
- 348
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3
votes
1 answer
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 (possibly empty) intersections.
So far, so standard. …
Jim
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3
votes
3 answers
Historical ways of *presenting* or axiomatizing the notion of a topological space
I've heard rumors in a couple of places that the modern presentation of a topology as $(X, \tau)$ where $X$ is our topological space and $\tau$ is our set of open sets is "somewhat" new and a simplification of how topologies used to be presented. We…
Greg Nisbet
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2
votes
0 answers
Development of the Idea of Homeomorphism?
How did the historical development of the notion of homeomorphism take place?
At first, I think the most important thing to study were continuous functions and metric structures.
When did the focus of mathematicians shift from metric to open sets?
Saikat
- 348
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1
vote
1 answer
Normed vector space : when and who?
When does the concept of "normed vector space" emerge?
Who is the first mathematician to consider this setting?
Colas
- 113
- 3
0
votes
0 answers
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 historical context behind the problem? More…
Humberto José Bortolossi
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