Definition that contains pure mathematics
- geometry the pure mathematics of points and lines and curves and surfaces
- arithmetic the branch of pure mathematics dealing with the theory of numerical calculations
- topology the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions
- analysis situs the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions
- set theory the branch of pure mathematics that deals with the nature and relations of sets