# 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 $X$.