How to show that $(0,1)$ and $[0,1)$ are not homeomorphic?
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
36315
Is $[0,1]$ a countable disjoint union of closed sets?
64454
$L^2([0,1])$ is a set of first category in $L^1([0,1])$?
95086
Homeomorphism is bijective
22869
Prove $[0, 1]$ and $(0, 1]$ are equinumerous by use of bijection
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
71173
Show that $\mathbb{A}^n$ on the Zariski Topology is not Hausdorff, but it is $T_1$
107076
Prove $S^1$ is not homeomorphic to $S^2$ using connectedness
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
10458
How to define a bijection between $(0,1)$ and $(0,1]$?
32765
$\mathbb{C}\mathbb{P}^1$ is homeomorphic to $S^2$
47231
The space $C^0([0;1],\mathbb{R})$ of all continuous, real-valued functions on $[0,1]$ is not reflexive.
146306
A continuous surjective function from $(0,1]$ onto $[0,1]$
1686
Show that quotient rings are not isomorphic
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
70712
How to prove that $k[x, xy, xy^2, \dotsc]$ is not noetherian?