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author committer bnewbold 2008-11-05 02:26:39 -0500 bnewbold 2008-11-05 02:26:39 -0500 0b113afaa8ae15d3672c6c50f6f6b5b26d78d618 (patch) 5d70cff07e574ac7166535f0e71bdb4430548de5 /math 5c146944cae9973731ae1b24f0161a1085e2c83e (diff) knowledge-0b113afaa8ae15d3672c6c50f6f6b5b26d78d618.tar.gzknowledge-0b113afaa8ae15d3672c6c50f6f6b5b26d78d618.zip
better for now
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-rw-r--r--math/topology54
1 files changed, 27 insertions, 27 deletions
 diff --git a/math/topology b/math/topologyindex 6b44484..79beeae 100644--- a/math/topology+++ b/math/topology@@ -17,20 +17,20 @@ subsets of :m:$A$ fufiling the criteria: 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 :m:$\mathcal{T}$ is - also in $\mathcal{T}$:m:.+ also in :m:$\mathcal{T}$. - 3. The intersection of a finite number of elements of $\mathcal{T}$:m: is- also in $\mathcal{T}$:m:.+ 3. The intersection of a finite number of elements of :m:$\mathcal{T}$ is+ also in :m:$\mathcal{T}$. -If a subset $B$:m: of $A$:m: is a member of $\mathcal{T}$:m: then-$B$:m: is an open set under the topology $\mathcal{T}$:m:.+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.-$\mathcal{T'}$:m: is finer than $\mathcal{T}$:m: if $\mathcal{T}$:m:-is a subset of $\mathcal{T'}$:m: (and $\mathcal{T}$:m: is coarser); -it is *strictly finer* if it is a proper subset (and $\mathcal{T}$:m: is -*strictly coarser*). Two sets are *comprable* if either $\mathcal{T\in T'}$:m:-or $\mathcal{T'\in T}$:m:.+: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*. @@ -41,35 +41,35 @@ Frequently Used Topologies *Standard Topology* The standard topology on the real line is generated by the collection of all intervals - `(a,b)=\{x|a