Newbetuts

How many connected components for the intersection $S \cap GL_n(\mathbb R)$ where $S \subset M_n(\mathbb R)$ is a linear subspace?

Show that a smooth map $F : M \rightarrow N$ has Constant rank if $F$ has a linear coordinate representation.

Deleting $n$ points from a connected space

Inverse image of connected set

Understanding proof that continuous image of connected is connected

Is any compact, path-connected subset of $\mathbb{R}^n$ the continuous image of $[0,1]$?

Prove that $\bigcap_{k = 1}^\infty C_k$ is also compact and connected. [duplicate]

Why is a bijection that preserves connectedness on $\mathbf{R}$ must be monotone?

Proving 2-sphere is not homeomorphic to plane

Product of totally disconnected space is totally disconnected?

A kind of converse to the Jordan curve theorem

In a Hausdorff space the intersection of a chain of compact connected subspaces is compact and connected

Show that $M = \{(x,y) \in \mathbb{R}^p \times \mathbb{R}^q : \lvert x \rvert = \lvert y \rvert \neq 0 \}$ is connected for $p,q \geq 2$

Cantor's Teepee is Totally Disconnected

Let $D$ be a bounded domain (open connected) in $ \mathbb C$ and assume that complement of $D$ is connected.Then show that $\partial D$ is connected

Prob. 2(b), Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The iff-condition for two points to be in the same component of $\mathbb{R}^\omega$

Property between totally disconnected and zero dimensional

If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $

New posts in connectedness

How many connected components for the intersection $S \cap GL_n(\mathbb R)$ where $S \subset M_n(\mathbb R)$ is a linear subspace?

Bourbaki exercise on connected sets

Is the following subset of a plane connected? (picture)

Show that a smooth map $F : M \rightarrow N$ has Constant rank if $F$ has a linear coordinate representation.

Deleting $n$ points from a connected space

Inverse image of connected set

Understanding proof that continuous image of connected is connected

Is any compact, path-connected subset of $\mathbb{R}^n$ the continuous image of $[0,1]$?

Prove that $\bigcap_{k = 1}^\infty C_k$ is also compact and connected. [duplicate]

Why is a bijection that preserves connectedness on $\mathbf{R}$ must be monotone?

Proving 2-sphere is not homeomorphic to plane

Product of totally disconnected space is totally disconnected?

A kind of converse to the Jordan curve theorem

In a Hausdorff space the intersection of a chain of compact connected subspaces is compact and connected

Show that $M = \{(x,y) \in \mathbb{R}^p \times \mathbb{R}^q : \lvert x \rvert = \lvert y \rvert \neq 0 \}$ is connected for $p,q \geq 2$

Cantor's Teepee is Totally Disconnected

Let $D$ be a bounded domain (open connected) in $ \mathbb C$ and assume that complement of $D$ is connected.Then show that $\partial D$ is connected

Prob. 2(b), Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The iff-condition for two points to be in the same component of $\mathbb{R}^\omega$

Property between totally disconnected and zero dimensional

If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $