FACTOID #151: The five countries with the highest coffee consumption are also the five countries whose citizens trust one another the most. Coincidence? Probably.
In topology and related areas of mathematics a gauge space is a topological space where the topology is defined by a family of pseudometrics. Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... In mathematics, an index set is another name for a function domain. ... In mathematics, a metric space is a set (or space) where a distance between points is defined. ...
A space is uniformizableif and only if it is a gauge space. In the mathematical field of topology, a uniform space is a set with a uniform structure. ... ↔ ⇔ ≡ logical symbols representing iff. ...
Examples
A metric space is trivially a gauge space as the topology is given by one metric.
A locally convex space, where the topology is given by a family of seminorms, is a gauge space as each seminorm induces a pseudometric.
Gauge theories became even more attractive when it was realized that non-abelian gauge theories reproduced a feature called asymptotic freedom, that was believed to be an important characteristic of strong interactions—thereby motivating the search for a gauge theory of the strong force.
Note that although gauge theory is dominated by the study of connections (primarily because it's mainly studied by high-energy physicists), the idea of a connection is not essential or central to gauge theory in general.
The space of smooth (although in physics, we often don't deal with smooth functions) sections of this bundle forms a principal homogeneous space of the group of gauge transformations.
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