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author committer bnewbold 2008-11-05 02:22:35 -0500 bnewbold 2008-11-05 02:22:35 -0500 5c146944cae9973731ae1b24f0161a1085e2c83e (patch) f72bf82a669b6263c140121ec9f52c170ffccbca /math a2d7b8c246db71e6c06e9f3db267b5a98691228d (diff) knowledge-5c146944cae9973731ae1b24f0161a1085e2c83e.tar.gzknowledge-5c146944cae9973731ae1b24f0161a1085e2c83e.zip
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 diff --git a/math/topology b/math/topologyindex c7e482f..6b44484 100644--- a/math/topology+++ b/math/topology@@ -8,15 +8,15 @@ Topology A *topological space* is a set for which a valid topology has been defined: the topology determines which subsets of the topological space are open and closed. In this way the-concept of open and closed subsets on the real number line (such as $(0,1)$:m: and-$[1,2]$:m:) are generalized to arbitrary sets.+concept of open and closed subsets on the real number line (such as :m:$(0,1)$ and+:m:$[1,2]$) are generalized to arbitrary sets. -Formally, a *topology* on a set $A$:m: is a collection $\mathcal{T}$:m: of -subsets of $A$:m: fufiling the criteria:+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 $A$:m: are both in $\mathcal{T}$:m:.+ 1. The empty set and the entire set :m:$A$:m: are both in :m:$\mathcal{T}$. - 2. The union of an arbitrary number of elements of $\mathcal{T}$:m: is + 2. The union of an arbitrary number of elements of :m:$\mathcal{T}$ is also in $\mathcal{T}$:m:. 3. The intersection of a finite number of elements of $\mathcal{T}$:m: is