Showing that $\mathbb{R}$ is connected
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
102598
Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
100437
Classification of connected subsets of the real line (up to homeomorphism)
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
102485
Showing that a topological space is ${\rm T}_1$
48557
Product of connected spaces
61375
Meaning of $\mathbb{R}[x]$
55486
Topological proof to show a complement set of a set is polygonally connected
116538
Proof of Connected Diagrams
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
121465
$R[x]$ has a subring isomorphic to $R$.
85332
Is $\mathbb{R}^4$ minus a line simply connected?
35069
Connectedness of the boundary
151719
Connected set in $\mathbb{S}^1$
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
158189
If $\{E_\alpha\}$ is connected, $\bigcap\limits_{\alpha\in A}E \neq \emptyset$, then $\bigcup\limits_{\alpha\in A}E$ is connected