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 diff --git a/math/topology.page b/math/topology.pagenew file mode 100644index 0000000..6f03eee--- /dev/null+++ b/math/topology.page@@ -0,0 +1,81 @@+====================+Topology+====================++.. warning:: Incomplete; in progress++.. note:: Most of the definitions and notation in the section are based on [munkres]_ ++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 :m:$(0,1)$ and+:m:$[1,2]$) are generalized to arbitrary sets.++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:$A$ are both in :m:$\mathcal{T}$.++ 2. The union of an arbitrary number of elements of :m:$\mathcal{T}$ is + also in :m:$\mathcal{T}$.++ 3. The intersection of a finite number of elements of :m:$\mathcal{T}$ is+ also in :m:$\mathcal{T}$.++If a subset :m:$B$ of :m:$A$ is a member of :m:$\mathcal{T}$ then+:m:$B$ is an open set under the topology :m:$\mathcal{T}$.++*Coarseness* and *Fineness* are ways of comparing two topologies on the same space.+:m:$\mathcal{T'}$ is finer than :m:$\mathcal{T}$ if :m:$\mathcal{T}$+is a subset of :m:$\mathcal{T'}$ (and :m:$\mathcal{T}$ is coarser); +it is *strictly finer* if it is a proper subset (and :m:$\mathcal{T}$ is +*strictly coarser*). Two sets are *comprable* if either :m:$\mathcal{T\in T'}$+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+============================++*Standard Topology*+ The standard topology on the real line is generated by the collection of all intervals + :m:`(a,b)=\{x|a