You may think that I am a real space cadet for talking about space today, but this is the way that I learn things and this post is not being written to make your heads explode. Space in Physics is a fundamental concept like time and mass. Space is where things happen, and spatial coordinates provide us with our reference system, they are necessary to define unique locations of any particular point or any object. At times it is hard to imagine space, I always tend to think about different shapes that relate to Geometry, and that makes sense as this subject is often defined as the mathematics of space. Space gives us the geometrical terms of distance or length, area and volume and this is sometimes called 1-dimensional, 2-dimensional or 3-dimensional space, however mathematicians often work in higher dimensional spaces. Terms for different types of space were developed to help us to understand complex phenomena. In mathematics, a space is a set (sometimes called a universe) with some added structure. Space is an abstract idea in math, it is extraordinarily general, but it is also a supremely important concept. In modern mathematics many different types of spaces are used, but the notion of “space” itself is not defined.
Space can be looked at as being a place for numerical variables, data structures or functions to exist and comprise points on a line, objects in a plane or in some higher dimensions of a universe. Space is a geometric structure, one that has its own mathematical entities and axioms that define it. Types of space include abstract space, affine space, ambient space, analytic space, anti-de Sitter space, Baire space, Banach space, Base space, Bergman space, Besov space, Borel space, Calabi-Yau space, Cartesian space, Cellular space, Chu space, compact space, connected space, configuration space, coordinate space, convex space, De Sitter space, Dirichlet space, Drinfeld’s Symmetric space, Eilenberg-Mac Lane space, Euclidean space, event space, feature space, Fiber space, Finsler space, First-Countable space, Fréchet space, function space, G-Space, Green space, Hardy space, Heisenberg space, Hilbert space, hyperbolic space, hypothetical space, Inner Product space, L2-Space, Lp space, Lens space, linear space, Liouville space, locally finite space, loop space, mapping space, measure space, metric space, minimal space, Minkowski space, moduli space, momentum space, Müntz space, noncommutative space, normed space, null space, outcome space, Paracompact space, phase space, physical space, planar space, Polish space, Poisson space, probability space, projective space, quotient space, real space, Riemannian space, sample space, Sobolev space, Standard space, State space, Stone space, subspace, Symplectic space, T2-Space, tangent space, Teichmüller space, Tensor Space, theory space, topological space, total Space, uniform space, vector space and virtual space. It is easy to get lost in a world that is comprised of so many exotic types of space, because math is often hidden in darkness, and obscured by an impenetrable cloud of symbols and jargon.
Space begins with the point, which is a 0-dimensional object that gives you a precise location or place on a plane. The most basic form of a space is a point and points can be combined or build up into a string of points which is where they eventually become lines, because lines are basically a series of points. Only a coherent arrangement of points makes up a space. Mathematics defines a space as being a set with some added structure. You could think of structures as places we do algebra, and spaces as places we do geometry in the same way that the human brain is split into an algebraic “left hemisphere” that thinks in logical sequences and a geometric “right hemisphere” that takes a more visual approach. Everything in the universe is part of a mathematical structure. All matter is made up of particles, which have properties and these properties are purely mathematical. Since space has properties such as dimensions, it is ultimately a mathematical structure. The everyday type of space familiar to most people is called Euclidean space. In Einstein’s theory of Special Relativity, Euclidean three-space plus time (the “fourth dimension”) are unified into the so-called Minkowski space. One of the most general type of mathematical spaces is the topological space.