Most topology texts go on directly to give definition of topology, then they give some examples and that's it, like they directly tell you right
Let $X$ be a set and let $τ$ be a family of subsets of $X$. Then $τ$ is called a topology on $X$ if:
- Both the empty set and $X$ are elements of $τ$
- Any union of elements of $τ$ is an element of $τ$
- Any intersection of finitely many elements of $τ$ is an element of $τ$
But why did we define it this way? What's the intuition?
Does anyone know a good text on topology which gives the intution behind the concepts, ...etc ?