13
votes
2answers
789 views

Who first defined _simply connected_, reference?

The following definition is due to Donald J. Newman: A connected open subset $D$ of the plane $\mathbb C$ is simply connected if and only if its complement $\widetilde D = \mathbb C \setminus D$ ...
19
votes
4answers
926 views

The role of ANR in modern topology

Absolute neighborhood retracts (ANRs) are topological spaces $X$ which, whenever $i\colon X\to Y$ is an embedding into a normal topological space $Y$, there exists a neighborhood $U$ of $i(X)$ in $Y$ ...
6
votes
3answers
650 views

Classification of Platonic solids

My question is very basic: where can I find a complete (and hopefully self-contained) proof of the classification of Platonic solids? In all the references that I found, they use Euler's formula ...
8
votes
3answers
555 views

Are k-spaces named for Kelley?

On page 58 of Mark Hovey's book Model Categories, he states the following definitions: "A subset $U$ of a space $X$ is compactly open if for every continuous $f:K\rightarrow X$ where $K$ is ...
3
votes
1answer
404 views

Klein Bottle exception to the Heawood Conjecture [duplicate]

Possible Duplicate: The Klein bottle and the Heawood Conjecture It is well known that the Heawood Conjecture states that the bound for the number of colours which are sufficient to colour a ...
2
votes
1answer
452 views

Meaning of “Compact” in 1932 Paper by van der Waerden “Continuity Theorem for Semisimple Lie Groups”.

I am putting together an exposition on Lie theory; maths research is not my day job, let alone real maths history, so apologies in advance for any ignorance shown by these questions. I am attempting ...
7
votes
1answer
1k views

Countable connected Hausdorff space

Let me start by reminding two constructions of topological spaces with such exotic combination of properties: 1) The elements are non-zero integers; base of topology are (infinite) arithmetic ...
33
votes
5answers
4k 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 ...