Questions tagged [topology]

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

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14
votes
1answer
872 views

How did Poincaré discover the fundamental group?

How did Poincare discover the fundamental group? What was the first instance that led Poincaré to discover this amazing theory?
12
votes
2answers
412 views

What examples led to the modern definition of a topological space?

Today the language of topological spaces via open sets is fundamental in many different areas of mathematics, and it is a bit mysterious that the same formalism successfully captures such a wide ...
9
votes
1answer
458 views

What caused the name change from “analysis situs” to “topology”?

J. Alexander's 1926 paper, Combinatorial Analysis Situs, doesn't refer to the field as combinatorial topology. He mentions that combinatorial analysis situs is concerned with topological invariants ...
4
votes
1answer
354 views

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 ...
6
votes
2answers
405 views

Did Gauss formulate, or at least know of, the full essence of the Gauss-Bonnet Theorem?

I know that a special case of the Bonnet theorem, called the Theorema Elegantissimum, was proved by Gauss in his 1827 treatise on differential geometry. This was a theorem that dealt with the ...