Newbetuts

Is the complement of an injective continuous map $\mathbb{R}\to \mathbb{R}^2$ with closed image necessarily disconnected?

Connectedness of the boundary

Is it true that a boundary of a simply connected and bounded set is connected in $\mathbb{C}$?

Can path connectedness be defined without using the unit interval?

Prove that the set of $n$-by-$n$ real matrices with positive determinant is connected

Prove that $(X\times Y)\setminus (A\times B)$ is connected

The closure of a connected set in a topological space is connected

Is the complement of countably many disjoint closed disks path connected?

What are the components and path components of $\mathbb{R}^{\omega}$ in the product, uniform, and box topologies?

Proof of "the continuous image of a connected set is connected"

Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected. [duplicate]

If $h : Y \to X$ is a covering map and $Y$ is connected, then the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$.

Why is this CW complex connected?

How to show that this space is not path connected?

$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?

Does path-connected imply simple path-connected?

New posts in connectedness

$\Gamma$ is a path connected

Why is the "topologist's sine curve" not locally connected?

connected manifolds are path connected

Connected, locally connected, path-connected but not locally path-connected subspace of the plane

Is the complement of an injective continuous map $\mathbb{R}\to \mathbb{R}^2$ with closed image necessarily disconnected?

Connectedness of the boundary

Is it true that a boundary of a simply connected and bounded set is connected in $\mathbb{C}$?

Can path connectedness be defined without using the unit interval?

Prove that the set of $n$-by-$n$ real matrices with positive determinant is connected

Prove that $(X\times Y)\setminus (A\times B)$ is connected

The closure of a connected set in a topological space is connected

Is the complement of countably many disjoint closed disks path connected?

What are the components and path components of $\mathbb{R}^{\omega}$ in the product, uniform, and box topologies?

Proof of "the continuous image of a connected set is connected"

Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected. [duplicate]

If $h : Y \to X$ is a covering map and $Y$ is connected, then the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$.

Why is this CW complex connected?

How to show that this space is not path connected?

$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?

Does path-connected imply simple path-connected?