# Tagged Questions

**13**

votes

**2**answers

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

**4**answers

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

**3**answers

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

**3**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**5**answers

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 ...