Example for path connected subspace of $\Bbb{R}^2$ that is not locally path connected at any point
55263
Path connected space that is not locally connected
136592
Examples of manifolds that are not boundaries
157830
Definition of locally pathwise connected
123430
Can a topological manifold be non-connected and each component with different dimension?
80524
Path-connected and locally connected space that is not locally path-connected
109462
Looking for a counter example for non-connected intersection of descending chain of closed connected sets
14345
If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected?
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
145668
Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
11301
Union of two vector subspaces not a subspace?
81220
Space which is connected but not path-connected
42811
Product of path connected spaces is path connected
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
151425
Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
28819
A union of two subspaces not equal to the vector space.
50645
Is the following set (path) connected?