diff options
Diffstat (limited to 'math/topology')
| -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 |