- #1
Ahmed Abdullah
- 203
- 3
Following is from Wolfram Mathworld
"A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions:
I am obviously new in topology and will be glad if you explain in basic term. I'd be specially interested to know how one differentiate between a straight line segment and a "Y" shaped graph using these definitions.
I have convinced myself of one way, please let me know if it is correct. I can separate Y naturally in three segment let's name them a,b and c.
Let X={a,b,c}.
So the topology Y on X will be { {},{a,b,c},{a,b},{a,c},{b,c},{a},{b},{c}}.
We can break a line segment on three part. Let's do likewise for line segment l.
So the topology l on X will be { {},{a,b,c},{a,b},{b,c},{b}}. Topology Y and l are on X and obviously different. :)
"A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions:
- The empty set is in T.
- X is in T.
- The intersection of a finite number of sets in T is also in T.
- The union of an arbitrary number of sets in T is also in T. " http://mathworld.wolfram.com/TopologicalSpace.html
I am obviously new in topology and will be glad if you explain in basic term. I'd be specially interested to know how one differentiate between a straight line segment and a "Y" shaped graph using these definitions.
I have convinced myself of one way, please let me know if it is correct. I can separate Y naturally in three segment let's name them a,b and c.
Let X={a,b,c}.
So the topology Y on X will be { {},{a,b,c},{a,b},{a,c},{b,c},{a},{b},{c}}.
We can break a line segment on three part. Let's do likewise for line segment l.
So the topology l on X will be { {},{a,b,c},{a,b},{b,c},{b}}. Topology Y and l are on X and obviously different. :)