Date: Jan 20, 2013 3:31 AM
Author: Kaba
Subject: Re: What is pi_0?
20.1.2013 1:37, W. Dale Hall wrote:

> Kaba wrote:

>> Hi,

>>

>> In this page

>>

>> http://en.wikipedia.org/wiki/Indefinite_orthogonal_group

>>

>> there is the notation pi_0 in the topology section. What does it refer

>> to? I don't see how the homotopy groups could cover n = 0...

>>

> Note that for two maps f,g : (S^0, *) --> (X,*) to b homotopic, there

> must be a path connecting the images f(+1) and g(+1) of the non-

> distinguished points in X. In short, the homotopy set of (X,*) is just

> the set of path-components of X. In general, pi_0(X,*) has a

> distinguished point consisting of the path-component of the point *.

Makes sense. Thanks.

--

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