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Answers

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38

What are some examples of ingenious, unexpected constructions?

1

Fair but irregular polyhedral dice

3

What is a continuous path?

2

When a Banach space is a Hilbert space?

2

What properties make $[0,1]$ a good candidate for defining fundamental groups?

3

Topological Characterisation of the real line.

2

How did “Ore’s Conjecture” become a conjecture?

1

Reference for the Gelfand-Neumark theorem for commutative von Neumann algebras

2

Direct construction of the integers

10

Uncountable family of infinite subsets with pairwise finite intersections

4

Is there an axiomatic approach of the notion of dimension ?

2

Self-dual normed spaces which are not Hilbert spaces

5

Orthogonality in non-inner product spaces

1

Reformulation of amenability and growth rate of a group in terms of general metric spaces.

2

Axiom of choice and convergence

1

Ultrafilters and principal filters

2

Representing a real number as the value of a countably infinite game

2

Can we have a finite cyclic group of rational numbers (under multiplication)?

1

A variational principle for amenable groups

1

Invariant means on commutative magmas

3

Why are Nash-Equilibria inside the Simplex S_n unique ?

5

What is the domain of the “average operator”?