From 7fb2bedfc29bb6a52520f280ce73b7491e071740 Mon Sep 17 00:00:00 2001 From: bnewbold Date: Wed, 5 Nov 2008 02:30:02 -0500 Subject: better for now --- math/topology | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) (limited to 'math') diff --git a/math/topology b/math/topology index 79beeae..6f03eee 100644 --- a/math/topology +++ b/math/topology @@ -2,7 +2,7 @@ Topology ==================== -.. note:: Incomplete; in progress +.. warning:: Incomplete; in progress .. note:: Most of the definitions and notation in the section are based on [munkres]_ @@ -14,7 +14,7 @@ concept of open and closed subsets on the real number line (such as :m:$(0,1)$ Formally, a *topology* on a set :m:$A$ is a collection :m:$\mathcal{T}$ of subsets of :m:$A$ fufiling the criteria: - 1. The empty set and the entire set :m:$A$:m: are both in :m:$\mathcal{T}$. + 1. The empty set and the entire set :m:$A$ are both in :m:$\mathcal{T}$. 2. The union of an arbitrary number of elements of :m:$\mathcal{T}$ is also in :m:$\mathcal{T}$. @@ -34,6 +34,7 @@ or :m:$\mathcal{T'\in T}$. *Smaller* and *larger* are somtimes used instead of finer and coarser. Topologies can be generated from a *basis*. + TODO: Hausdorf Frequently Used Topologies @@ -42,6 +43,7 @@ Frequently Used Topologies *Standard Topology* The standard topology on the real line is generated by the collection of all intervals :m:`(a,b)=\{x|a