Recent content by oxeimon

Sorry maybe I wasn't clear. I meant to begin by "fixing" a particular generator g. We then can call this g by the name "1". We'll call (g+g) = 2g by the name "2", (g+g+g) = 3g by the name "3", and so on, with pg = 0. To see that it's commutative, say we want to multiply 2*3 in the group of...

Is there an easy way to define a field by only using one operation? It's easy to see that a cyclic abelian group of prime order uniquely defines a field if you consider multiplication as just repeated addition. Ie, consider such a group G with generator g , identity e with order p . Then...

Aren't these the same topologies? If x = (a+b)/2, e = (a-b)/2, then (a,b) = (x-e,x+e) So I guess the "usual topology" on \mathbb{R} is just the "euclidean metric"?

On another note, can someone prove that for any two points x \ne y, we have that the intersection B(x)\cap B(y) is not itself an \epsilon-ball? why is the epsilon so high up? I used "\epsilon" ...

So I'm trying to teach myself some topology, and the first thing I noticed, was that a metric space is a topological space under the topology of all open balls.. But then, consider the intersection of two open balls, can someone prove to me that the result is another open ball? Or do they...