# General topology software or how to put into mathematica

Posted 9 years ago
3477 Views
|
|
2 Total Likes
|
 Hi all, is there a software which could enumerate all possible topology defined by x = {a,b,c}, and show them on the screen. if its possible to implement in mathematical how to do it ?
 There is no built in function to do this, but it's not too difficult to program for a discrete set of values:To build it up, I'd first make a function that gives every possible union and intersection of the values of a set: everyPossibleUnion[set_] := Union@Map[Union @@ # &, Subsets[set, {1, Infinity}]] everyPossibleIntersection[set_] := Union@Map[Intersection @@ # &, Subsets[set, {1, Infinity}]] From there you can make a function which tests if a set is a topology by basically stating the definition: mySet = {1, 2, 3, 4} TopologyQ[pset_] := SubsetQ[pset, {{}, mySet}] && SubsetQ[pset, everyPossibleUnion[pset]] && SubsetQ[pset, everyPossibleIntersection[pset]] I think I've done this right. It seems to work okay. indiscreteTopology = {{}, mySet} TopologyQ[indiscreteTopology] True discreteTopology = Subsets@mySet; TopologyQ[discreteTopology] True exTopology = {{}, {2}, {1, 2}, {2, 3}, {1, 2, 3}, {1, 2, 3, 4}}; TopologyQ[exTopology] True notATopology = {{}, {1, 2}, {2, 3}, {1, 2, 3, 4}} TopologyQ[notATopology] False