Thread: Easier way to look at topologies?

I am having a really hard time grasping the idea of Topologies of a set. I understand the 3 rules for a topology but I get lost when I get something like this:

T = {{},{1},{3},{1,3},{1,2,3}} is a topology on X = {1,2,3}

How and why? Is there an easier way to look at this concept?

Originally Posted by Bman900

I am having a really hard time grasping the idea of Topologies of a set. I understand the 3 rules for a topology but I get lost when I get something like this:

T = {{},{1},{3},{1,3},{1,2,3}} is a topology on X = {1,2,3}

How and why? Is there an easier way to look at this concept?

unfortunately, not really. you have to get comfortable with the basic definition. it might seem crude, but it was made up so that certain things would work.

of course, T is a topology on {1,2,3} because it satisfies the three axioms.

(1) the empty set and the set itself are in T

(2) The union of any number of elements in T is also in T

(3) The intersection of any (finite) collection of sets in T is in T.

Well to be honest you gave me a better definition then my teacher. Now for neighbor hoods. He talked about something along this:
A set V X is called a neighboor hood of X if there exists a set G T such that X G V

So does this mean if X belongs to G while G is a subset of V then G and V are neighboorhoods of X?

You asked about topologies and said you knew the "3 rules for a topology". But your last post talks about neighborhoods rather than topologies. And what 3 rules are you referring to?