From 0b113afaa8ae15d3672c6c50f6f6b5b26d78d618 Mon Sep 17 00:00:00 2001
From: bnewbold
Date: Wed, 5 Nov 2008 02:26:39 -0500
Subject: better for now
---
math/topology | 54 +++++++++++++++++++++++++++---------------------------
1 file changed, 27 insertions(+), 27 deletions(-)
(limited to 'math')
diff --git a/math/topology b/math/topology
index 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