List questions from connectedness | MathQa

Show that there exist $f$ such that $[f(z)]^2=(z-a)(z-b)$

Published on 12 Jan 2025 - 22:09

Is The subspace of $M_{m\times n}(\mathbb C)$ consisting of all matrices of rank equal to $k$ is connected?

Published on 12 Jan 2025 - 22:31

If $f$ is continuous and $A$ is path-connected, then $f^{-1}(A)$ path-connected

Published on 12 Jan 2025 - 22:20

A line is simply connected but a circle is not. Does this mean that the one-point compactification of the real line is not simply connected?

Published on 12 Jan 2025 - 22:21

Prove that on every great circle on the earth there are antipodal points at which the temperature is the same.

Published on 12 Jan 2025 - 22:26

Direct proof for intervals in $\mathbb{R}$

Published on 12 Jan 2025 - 22:00

$O$ is connected if and only if every two points $x,y\in O, x\ne y,$ are connected by a piecewise linear path

Published on 12 Jan 2025 - 22:26

Connected Properties of an Interval Set

Published on 28 Dec 2024 - 12:25

Proving a mangled graph to be connected.

Published on 12 Jan 2025 - 22:27

Is the interval $[a,b]$ connected with discrete metric?

Published on 12 Jan 2025 - 22:18