Space for mathematicians is an interesting set. Or we can say a set with structure. Trying to get used to this concept, I am listing a few spaces, with some explanation, here. By the way, members of such sets are usually called points.
- Vector Space: members of such a space can be scaled and added. Here the definition is dependent on properties of the members.
- Topological Space: in this space points have neighbourhoods. Or, the topological space is a set on which a collection of open sets (closed under unions and finite intersections) is defined.
- State Space: This means different things to computer scientists, physicists, and control engineers. For control engineers, state space is the space in which members are tuples of state variables.
- Metric Space: a metric or distance is defined between members of such a space.
- Euclidean Space: for most of us, this is the space acquired by age eighteen.