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Results tagged with gn.general-topology
Search options questions only
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user 6094
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
67
votes
22
answers
10k
views
When has discrete understanding preceded continuous?
From my limited perspective, it appears that the understanding
of a mathematical phenomenon has usually been achieved,
historically, in a continuous setting
before it was fully explored in a discrete …
140
votes
7
answers
34k
views
Is the boundary $\partial S$ analogous to a derivative?
Without prethought, I mentioned in class once that the reason the symbol $\partial$
is used to represent the boundary operator in topology is
that its behavior is akin to a derivative.
But after refle …
- 151k
26
votes
0
answers
354
views
Can 4-space be partitioned into Klein bottles?
It is known that $\mathbb{R}^3$ can be partitioned into disjoint circles,
or into disjoint unit circles, or into congruent copies of a real-analytic curve
(Is it possible to partition $\mathbb R^3$ in …
- 151k
8
votes
1
answer
922
views
Filling $\mathbb{R}^3$ with skew lines
I would like to know if it is possible to fill $\mathbb{R}^3$ with lines with the
following two properties:
(1) Every point $x \in \mathbb{R}^3$ is contained in precisely one line.
(2) Every neighbo …
- 151k
50
votes
3
answers
8k
views
Thurston's 24 questions: All settled?
Thurston's 1982 article on three-dimensional manifolds1 ends with $24$ "open questions":
$\cdots$
Two naive questions from an outsider:
(1) Have all $24$ now been resolved?
(2) If so, w …
- 151k
8
votes
3
answers
1k
views
Is the list of "known" 3D compact manifolds complete?
"it is an open question if the known compact manifolds in 3-D are complete."
This is a quote from Eric Weisstein's
CRC Concise Encyclopedia of Mathematics, Second Edition. 2010, p.480.
(Google Bo …
- 27.5k