# Tagged Questions

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### proving that $SO(n)$ is path connected

Our professor gave us exercise to show that $G=SO(n,\mathbb R)$ is path connected. He gave some hints, using them I have come upto this far: I have shown that $SO(n)$ acts on $S^{n-1}$ transitively ...
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### Definition of a topological module

A topological universal algebra of type $\Omega$ is a universal algebra $A$ of type $\Omega$ that is also a topological space, such that for any $n\!\in\!\mathbb{N}$ and any operation ...
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### Topological fields questions

From Wikipedia: "Let $K$ be a topological field, namely a field with a topology such that addition, multiplication, and division are continuous. In most applications $K$ will be either the field of ...
I'm wondering about the following: Let$\ X$ be a topological vector space. Then one could pick balanced neighborhoods$\ W$ and$\ U$ of$\ 0$ such that $\ \overline{U} + \overline{U} \subset W$, ...
Let $K$ be a topological field. Let $V$ be a topological vector space over $K$ (if it makes things convenient, you may assume it is finite dimensional). Naive Question: Is there a canonical way of ...