Space (math)

A space is a set, with additional structure. 
I think 'space' tends to refer to vector spaces in the examples below? No: vector spaces a types of spaces. 
Note necessarily; a topological space is not a vector space per se? 
== Definition ==
== Types of spaces ==
Add some collects of spaces by characteristics that are useful
== List of spaces ==
* Euclidean space
*Metric space
*Vector space
*Normed vector space
*Topological space
*Inner product space
*Hausdorff space
* L^p-space
* Banach space
* Hilbert space
*Manifold
*Algebra (the ones below are the additional structures, not the spaces themselves? E.g. for algebra, the space would be 'field of sets'?)
*Sigma-algebra
*Pi-system
*Lambda-system
*
Add a table with types of conditions and how the different definitions of spaces satisfy conditions.
== Overview of spaces ==
The image below gives an overview of different mathematical spaces. The colors correspond with the domain of mathematics it would most likely be found in. Yellow: topology, blue: algebra, green: analysis, orange: manifold theory.By Eric Platt. Found here: https://mathematicalspaces.quora.com/A-Map-of-Mathematical-Spaces