$A=\mathbb{R}^n-\{a\}$ for some $a\in \mathbb{R}^n$ is path connected
36044
Show $\Bbb R ^n$ with a finite set removed is still connected.
80524
Path-connected and locally connected space that is not locally path-connected
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
1453
Prove that the graph is connected
97781
invertible matrices connected or not
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
30079
Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
101712
Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
12104
How to prove this result involving the quotient maps and connectedness?
31266
Proof of "the continuous image of a connected set is connected"
102598
Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
151425
Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
127365
Question on showing a bijection between $\pi_1(X,x_0)$ and $[S^1, X]$ when X is path connected.
27253
Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$
116866
$A\times B$ connected component implies $A,B$ connect components
28500
What are the components and path components of $\mathbb{R}^{\omega}$ in the product, uniform, and box topologies?
113915
A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$