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 diff --git a/math/topology b/math/topologynew file mode 100644index 0000000..104cbe8--- /dev/null+++ b/math/topology@@ -0,0 +1,79 @@+====================+Topology+====================++.. note:: 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 $(0,1)$:latex: and+$[1,2]$:latex:) are generalized to arbitrary sets.++Formally, a *topology* on a set $A$:latex: is a collection $\mathcal{T}$:latex: of +subsets of $A$:latex: fufiling the criteria:++ 1. The empty set and the entire set $A$:latex: are both in $\mathcal{T}$:latex:.++ 2. The union of an arbitrary number of elements of $\mathcal{T}$:latex: is + also in $\mathcal{T}$:latex:.++ 3. The intersection of a finite number of elements of $\mathcal{T}$:latex: is+ also in $\mathcal{T}$:latex:.++If a subset $B$:latex: of $A$:latex: is a member of $\mathcal{T}$:latex: then+$B$:latex: is an open set under the topology $\mathcal{T}$:latex:.++*Coarseness* and *Fineness* are ways of comparing two topologies on the same space.+$\mathcal{T'}$:latex: is finer than $\mathcal{T}$:latex: if $\mathcal{T}$:latex:+is a subset of $\mathcal{T'}$:latex: (and $\mathcal{T}$:latex: is coarser); +it is *strictly finer* if it is a proper subset (and $\mathcal{T}$:latex: is +*strictly coarser*). Two sets are *comprable* if either $\mathcal{T\in T'}$:latex:+or $\mathcal{T'\in T}$:latex:.+*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 + `(a,b)=\{x|a