Path connectedness of the set of points $(x,y)$ where $x$ is rational or $y$ is rational
15865
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
89264
Connectedness in the Quotient Space
102084
How to show path-connectedness of $GL(n,\mathbb{C})$
144383
The closure of a connected set in a topological space is connected
62260
Rational Coordinates with two intersecting lines
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
133633
A question about path-connected and arcwise-connected spaces
18572
Union of a family of connected pairwise not disjoint subspaces is connected
100437
Classification of connected subsets of the real line (up to homeomorphism)
89164
When is the graph of the divisor relation on $[n]$ planar?
116538
Proof of Connected Diagrams
122487
Degree of Rational Function
102484
Connectedness problem and countability of compact subsets of the Sorgenfrey line
17470
Does path-connected imply simple path-connected?
116494
What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?