Subspace of a seperable space is not neccessarily seperable in topology space
10034
Give an example of a non-separable subspace of a separable space
80524
Path-connected and locally connected space that is not locally path-connected
63697
connected subspaces need to lie in one separated component
151950
Why is indiscrete topology unmetrizable?
35305
Why is $\mathbb{R}^2$ not a subset and /or a subspace of $\mathbb{R}^3$?
90816
Why does the product topology allow proper subsets for only finitely many elements?
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
137438
Restrict a metric, gives same topology as subspace topology from larger space $X$
110832
$F_\sigma$-subsets in a normal space can be separated
7069
On the product of $\mathfrak c$-many separable spaces
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
107000
Dimension of intersection of distinct subspaces
149426
Is there a Hausdorff space $X$ separating points of any Hausdorff space?
11301
Union of two vector subspaces not a subspace?
111001
Does weak topology preserve topological vector space structure?
4717
The union of linear subspaces is not necessarily a subspace
84148
Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?