Uniform topology
Encyclopedia
In mathematics
, the uniform topology on a space has several different meanings depending on the context:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the uniform topology on a space has several different meanings depending on the context:
- In functional analysis, it sometimes refers to a polar topology on a topological vector space.
- In general topology, it is the topology carried by a uniform spaceUniform spaceIn the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence.The conceptual difference between...
. - In real analysis, it is the topology of uniform convergence.