Is $\{(0,0)\}\cup\{(x,\sin{1\over x}):x\in\mathbb{R},x>0\}$ path connected?
12405
Topologist's sine curve is not path-connected
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
27581
Topologist's sine curve is connected
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
84492
Can $X$ have compact connected components?
102084
How to show path-connectedness of $GL(n,\mathbb{C})$
55902
Show $R[x]/(x)\cong R$
33190
Show that the complex integral is zero for any closed, piece wise smooth path
57943
If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
2575
Showing that $\mathbb{R}$ is connected
67088
Closure and pathwise connected
60485
Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$
101712
Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
30079
Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
97213
Why does $\sin(0)$ exist?
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
68234
Is $[0,1) \cup \{2\}$ a manifold with boundary? My issue is the $2$.