I am taking a course in intro topology and very confused because the lecturer has only given us a definition of metric topology while all the texts I have read have the axiomatic definition of topology.
I don't think they are the samee but what is the difference? Also is metric topology same as 'discrete topology'?
Definitions I have are:
Metric topology: Collection of open sets such that all subsets are in X.
Topology: The three axioms of it should contain X, empty set, union and intersectoin should be in the topology.
Discrete topology: T is the collection of all subsets of a non empty set X.
To me discrete and metric look the same?
I am not understanding anything in lectures so I am trying to teach myself with resources online. Thanks for your help.