Show that the letters X and I (thought of as topological spaces) are not homeomorphic
128780
What does "removing a point" have to do with homeomorphisms?
139176
The real line is not homeomorphic to any non-trivial product space
131890
Totally disconnected space that is not $T_2$
49147
Showing that the class of all sets of a particular cardinality is not a set.
67383
Prove that $G'$ is not planar.
112306
Two manifolds $X$ and $Y$ with two bijective continuous functions from $X$ to $Y$ and $Y$ to $X$, but not homeomorphic
107389
Show that the vector space of real functions is not finitely spanned
46970
If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism.
27933
Show that unit circle is not homeomorphic to the real line
57310
Prove $\mathbb{Z}$ is not a vector space over a field
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
70082
Show: Quotient space is homeomorphic to unit sphere
113534
Show that any metrizable space $X$ is Hausdorff
65180
A compact Hausdorff space that is not metrizable
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
33140
Two non-homeomorphic spaces with continuous bijective functions in both directions