Today I Learned

Some of the things I've learned every day since Oct 10, 2016

78: 2 Simple Topological Spaces

Using the open set definition of a topology as a pair (X, \tau), where X is a set and \tau is a collection of subsets of X satisfying certain axioms, if X is non-empty and finite then we immediately can define 2 simple and valid topologies on it:

  1. \tau = P(X), the power set of X
  2. \tau = \{\O , X\}, the empty set and X itself

The former is called the discrete topology on X, and the latter is called the trivial topology on X.


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