New posts in general-topology

An example of a non-paracompact topological space

Does a map between topologies determine a map between sets?

What differences would it make to live in $T^3$, in $S^2 \times S^1$, in $\mathbb{R}P^3$, or in $S^3$?

The quotient space $S^3/S^1$ is homeomorphic to $S^2$

Compact metric space group $Iso(X,d)$ is also compact

Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable

Is a path connected covering space of a path connected space always surjective?

Topological spaces in which a set is the support of a continuous function iff it is the closure of a open set.

Connectedness of a certain subset of the plane

$f$ continuous iff $\operatorname{graph}(f)$ is compact

Where can I find more insight about spaces of subsets of a base space?

Contracting a contractible set in $\mathbb R^2$

Prove that $\mathbb{N}$ with cofinite topology is not path-connected space.

Is this proof that all metric spaces are Hausdorff spaces correct?

Is the punctured plane homotopy equivalent to the circle?

sphere-filling curve

How to show that disjoint closed sets have disjoint open supersets?

Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$

Pseudo metric spaces are not Hausdorff.

Path Connectedness and continuous bijections