Can $\mathbb{R}$ be homeomorphic to some $X \times X$?
88051
$\mathbb R = X^2$ as a Cartesian product
128989
Is ${\bf Z} \times {\bf Z}$ elementarily equivalent to ${\bf Z}$?
22890
Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$?
144246
Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
94059
Extending a Homotopy from $X \times [0,1]$ to $X \times \mathbb{R}$
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
40490
Birational isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
77563
Homeomorphism between spaces equipped with cofinite topologies
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
82458
Homeomorphism between the unit disc and the unit square
82814
Homework question on whether two quotient spaces are homeomorphic
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$