From ab8b60e77216a62216ac0841716a9c3f4f781df0 Mon Sep 17 00:00:00 2001
From: bnewbold <bnewbold@robocracy.org>
Date: Sun, 24 Jan 2010 08:23:12 +0000
Subject: fixes

---
 math/topology.page | 37 +++++++++++++++++--------------------
 1 file changed, 17 insertions(+), 20 deletions(-)

(limited to 'math')

diff --git a/math/topology.page b/math/topology.page
index ea369fb..9701427 100644
--- a/math/topology.page
+++ b/math/topology.page
@@ -26,8 +26,8 @@ $B$ is an open set under the topology $\mathcal{T}$.
 $\mathcal{T'}$ is finer than $\mathcal{T}$ if $\mathcal{T}$
 is a subset of $\mathcal{T'}$ (and $\mathcal{T}$ is coarser); 
 it is *strictly finer* if it is a proper subset (and $\mathcal{T}$ is 
-*strictly coarser*). Two sets are *comprable* if either $\mathcal{T\in T'}$
-or $\mathcal{T'\in T}$.
+*strictly coarser*). Two sets are *comprable* if either $\mathcal{T \in T'}$
+or $\mathcal{T' \in T}$.
 *Smaller* and *larger* are somtimes used instead of finer and coarser.
 
 Topologies can be generated from a *basis*. 
@@ -37,42 +37,39 @@ TODO: Hausdorf
 Frequently Used Topologies
 ============================
 
-*Standard Topology*
-    The standard topology on the real line is generated by the collection of all intervals 
+Standard Topology
+:    The standard topology on the real line is generated by the collection of all intervals 
     $$(a,b)=\{x|a<x<b\}$$
-
     This is the usual definition for open sets on the real line.
 
-*Discrete Topology*
-    The topology on a set $A$ consisting of all points of $A$;
+Discrete Topology
+:    The topology on a set $A$ consisting of all points of $A$;
     in other words the power set of $A$.
 
-*Trivial/Indiscrete Topology*
-    The topology on a set $A$ consisting of only the empty set and $A$
+Trivial/Indiscrete Topology
+:    The topology on a set $A$ consisting of only the empty set and $A$
     itself. Not super interesting but it's always there (when $A$ isn't empty).
     
-*Finite Complement Topology* ($\mathcal{T}_f$)
-    The topology on a set $A$ consisting of the empty set any subset 
+Finite Complement Topology ($\mathcal{T}_f$)
+:    The topology on a set $A$ consisting of the empty set any subset 
     $U$ such that $A-U$ has a finite number of elements.
 
-*Lower Limit Topology* ($\mathbb{R}_{\mathcal{l}}$)
-    The lower limit topology on the real line is generated by the collection of all half open
+Lower Limit Topology ($\mathbb{R}_{\mathcal{l}}$)
+:    The lower limit topology on the real line is generated by the collection of all half open
     intervals
     $$[a,b)=\{x|a\leq x<b\}$$
     $\mathbb{R}_{\mathcal{l}}$ is strictly finer than the standard topology and
     is not comprable to $\mathbb{R}_K$.
 
-*K-Topology* ($\mathbb{R}_K$)
-    Let $K$ denote the set of all numbers $1/n$ where $n$ is
+K-Topology ($\mathbb{R}_K$)
+:    Let $K$ denote the set of all numbers $1/n$ where $n$ is
     a positive integer. 
     The K-topology on the real line is generated by the collection of all standard open intervals 
     minus $K$. 
     $\mathbb{R}_K$ is strictly finer than the standard topology and is not
     comprable to $\mathbb{R}_{\mathcal{l}}$.
 
-*Order Topology*
-    TODO
-
-
+Order Topology
+:    TODO
 
-[^munkres] **Topology (2nd edition)**, by James R. Munkres.
+[^munkres]: **Topology (2nd edition)**, by James R. Munkres.
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