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author | bnewbold <bnewbold@eta.mit.edu> | 2008-11-05 02:22:35 -0500 |
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committer | bnewbold <bnewbold@eta.mit.edu> | 2008-11-05 02:22:35 -0500 |

commit | 5c146944cae9973731ae1b24f0161a1085e2c83e (patch) | |

tree | f72bf82a669b6263c140121ec9f52c170ffccbca /math | |

parent | a2d7b8c246db71e6c06e9f3db267b5a98691228d (diff) | |

download | knowledge-5c146944cae9973731ae1b24f0161a1085e2c83e.tar.gz knowledge-5c146944cae9973731ae1b24f0161a1085e2c83e.zip |

blah, syntax?

Diffstat (limited to 'math')

-rw-r--r-- | math/topology | 12 |

1 files changed, 6 insertions, 6 deletions

diff --git a/math/topology b/math/topology index c7e482f..6b44484 100644 --- a/math/topology +++ b/math/topology @@ -8,15 +8,15 @@ Topology 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 `$(0,1)$`:m: and -`$[1,2]$`:m:) are generalized to arbitrary sets. +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 `$A$`:m: is a collection `$\mathcal{T}$`:m: of -subsets of `$A$`:m: fufiling the criteria: +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 `$A$`:m: are both in `$\mathcal{T}$`:m:. + 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 `$\mathcal{T}$`:m: is + 2. The union of an arbitrary number of elements of :m:`$\mathcal{T}$` is also in `$\mathcal{T}$`:m:. 3. The intersection of a finite number of elements of `$\mathcal{T}$`:m: is |