Prove that $\mathbb{R}\not\cong X\times X$ for any $X$
139176
The real line is not homeomorphic to any non-trivial product space
90055
Show that $\mathcal P(x)\notin x$
11259
Prove $R\times S$ is not an integral domain
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
8374
How to prove that $R/I \otimes_R M \cong M / IM$
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
76048
Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$?
46771
$X$ is homeomorphic to $X\times X$ (TIFR GS $2014$)
69046
Proof of $\mathbb{Q}$ is not cyclic
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
83023
From axiom of regularity, how can I prove $x \notin y \lor y \notin x$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
1686
Show that quotient rings are not isomorphic
95686
$Lie(G \times H)\cong Lie(G)\oplus Lie(H)$
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$