New posts in Open Map

How to prove that the induced topology is the coarsest and identification topology is the finest topology that keeps the map continuous?

Show that an open linear map between normed spaces is surjective.

Let $Y$ be a finite-dimensional normed space, $X$ a normed space, and $T: X \to Y$ a surjective linear operator. Show that $T$ is an open mapping.

continuous image of a locally compact space is locally compact

When is the quotient space of a second countable space second countable?

Intuition for an open mapping

Example of quotient mapping that is not open