The separation-axioms tag has no usage guidance.

**0**

votes

**0**answers

57 views

### Can a countable and connected space be hausdorf? [duplicate]

Can a countable and connected space be hausdorf? If not, can it be T1, i.e., every pair of points is topologically distinguishable and seperable?

**2**

votes

**1**answer

75 views

### Separating Differences of Open Sets

Has anyone ever considered something like the following separation axiom?
$(*)$ For any pair of open sets $O$ and $N$, there exist disjoint open sets containing $O\setminus N$ and $N\setminus O$.
...

**2**

votes

**1**answer

346 views

### Browder's fixed point theorem in non-Hausdorff topological vector spaces

Browder proved the following fixed point theorem in his 1968 Mathematische Annelen paper (Theorem 1):
Theorem. Let $K$ be a non-empty compact convex subset of a topological vector space $E$ (where we ...

**3**

votes

**2**answers

546 views

### Separation axioms

Reading about separation axioms, I wonder:
Is there a separation axiom weaker than $T_2$ but stronger than $T_1$? $T_{1.5}$?
I suppose there are some separation axioms stronger that $T_6$, how many ...

**6**

votes

**1**answer

594 views

### Stack with affine stabilizers but not quasi-affine diagonal

Give an example of a stack X with affine stabilizer groups and separated but not quasi-affine diagonal.
Remarks:
1) If X has finite stabilizer groups then the diagonal is quasi-finite and separated, ...