Let $\lVert\cdot\rVert_1,\lVert\cdot\rVert_2$ be norms on vector space $X$. Prove that they generate the same topology iff they are equivalent.
99350
Are two norms equivalent if they induce the same topology on a vector space?
62425
Equivalent Definitions of the Operator Norm
116273
Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
139272
On the norm of a quotient of a Banach space.
15839
equivalent norms in Banach spaces of infinite dimension
98759
Proof of "Dual normed vector space is complete"
57619
Norms Induced by Inner Products and the Parallelogram Law
108864
Showing that two topologies give rise to the same topology
102485
Showing that a topological space is ${\rm T}_1$
137438
Restrict a metric, gives same topology as subspace topology from larger space $X$
62342
$x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
42913
Equivalence of the definition of the Subbasis of a Topology
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
87265
If $(A-\lambda{I})$ is $\lambda$-equivalent to $(B-\lambda{I})$ then $A$ is similar to $B$
104881
Showing that two Banach spaces are homeomorphic when their dimensions are equal.
151910
Why is $K^{\ast n}$ contained in the norm group?
133820
The product topology on $\mathbb R_d\times \mathbb R$ vs. the dictionary order topology on $\mathbb R\times \mathbb R$