- #1

Ahmed Abdullah

- 203

- 3

"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. :)