Show that $\mathbb{T}^1 \cong \mathbb{C}^*/\mathbb{R}_{>0}$
58707
Prove Quotient Group Isomorphism
116630
Antiderivative $1/z$ on $\mathbb C$
42883
Cross product in $\mathbb R^n$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
33196
show that A(T) is a group under operation of composition of functions
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
33642
Finite dimensional subspace of $C([0,1])$
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
137011
showing $\psi: R\to \mathbb C$ is ring isomorphism.
66866
Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
93606
Showing that $C[0,1]$ is not complete
31710
Show that $\mathcal{J}=\{[a, a+1) \mid a \in \mathbb{R}\}$ generates the Borel set of $\mathbb{R}$
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
102485
Showing that a topological space is ${\rm T}_1$
51898
Show that $\operatorname{Hom}_{R} (R,M) \cong M$
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$