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An example of a non-paracompact topological space
general-topology
examples-counterexamples
paracompactness
Does a map between topologies determine a map between sets?
general-topology
elementary-set-theory
What differences would it make to live in $T^3$, in $S^2 \times S^1$, in $\mathbb{R}P^3$, or in $S^3$?
general-topology
The quotient space $S^3/S^1$ is homeomorphic to $S^2$
general-topology
topological-groups
Compact metric space group $Iso(X,d)$ is also compact
general-topology
metric-spaces
compactness
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
general-topology
Is a path connected covering space of a path connected space always surjective?
general-topology
algebraic-topology
covering-spaces
Topological spaces in which a set is the support of a continuous function iff it is the closure of a open set.
general-topology
continuity
Connectedness of a certain subset of the plane
general-topology
$f$ continuous iff $\operatorname{graph}(f)$ is compact
general-topology
continuity
compactness
Where can I find more insight about spaces of subsets of a base space?
general-topology
uniform-spaces
continuum-theory
Contracting a contractible set in $\mathbb R^2$
general-topology
reference-request
algebraic-topology
Prove that $\mathbb{N}$ with cofinite topology is not path-connected space.
general-topology
analysis
Is this proof that all metric spaces are Hausdorff spaces correct?
general-topology
metric-spaces
proof-verification
Is the punctured plane homotopy equivalent to the circle?
general-topology
homotopy-theory
sphere-filling curve
general-topology
geometry
How to show that disjoint closed sets have disjoint open supersets?
general-topology
metric-spaces
Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$
general-topology
connectedness
Pseudo metric spaces are not Hausdorff.
general-topology
Path Connectedness and continuous bijections
general-topology
continuity
connectedness
abstract-algebra
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