Is every dense subspace of a separable space separable?
10034
Give an example of a non-separable subspace of a separable space
134859
Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf implies that $X$ is separable.
67702
Minimal dense subset
18039
Let $A$ be a dense subset of $X$ and suppose $A$ is connected in the induced subspace topology, then $X$ is also connected
8557
Invertible Matrices are dense
4717
The union of linear subspaces is not necessarily a subspace
69766
Is every normed vector space, an inner product space
86325
Is an increasing union of subspaces a subspace?
19856
Prove that a subset of a separable set is itself separable
128934
Every infinite Hausdorff space has an infinite discrete subspace
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space
78082
Dense subset of two Banach spaces also dense in the intersection
67191
When is the union of a family of subspaces of a vector space also a subspace?
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
120135
Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets
28804
No. of possible dense subsets of a metric space
30796
Is the set of irrationals separable as a subspace of the real line?