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author committer bnewbold 2008-11-05 02:30:02 -0500 bnewbold 2008-11-05 02:30:02 -0500 7fb2bedfc29bb6a52520f280ce73b7491e071740 (patch) c8f5d0cf823f5ba7383c21c84e2a72b5ddedf12a /math 0b113afaa8ae15d3672c6c50f6f6b5b26d78d618 (diff) knowledge-7fb2bedfc29bb6a52520f280ce73b7491e071740.tar.gzknowledge-7fb2bedfc29bb6a52520f280ce73b7491e071740.zip
better for now
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-rw-r--r--math/topology14
1 files changed, 8 insertions, 6 deletions
 diff --git a/math/topology b/math/topologyindex 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