# Locally Convex

### Some articles on locally convex, convex:

Discontinuous Linear Map - Beyond Normed Spaces
... but there exist infinite dimensional locally convex topological vector spaces such that every functional is continuous ... other hand, the Hahn–Banach theorem, which applies to all locally convex spaces, guarantees the existence of many continuous linear functionals, and so a large dual space ... In fact, to every convex set, the Minkowski gauge associates a continuous linear functional ...
Cartan–Hadamard Theorem - Metric Geometry - Generalization To Locally Convex Spaces
... Call a metric space X convex if, for any two constant speed minimizing geodesics a(t) and b(t), the function is a convex function of t ... A metric space is then locally convex if every point has a neighborhood that is convex in this sense ... The Cartan–Hadamard theorem for locally convex spaces states If X is a locally convex complete connected metric space, then the universal cover of X is a convex geodesic space with respect to the induced length ...
Locally Convex Topological Vector Space - Examples and Nonexamples - Examples of Spaces Lacking Local Convexity
... Many topological vector spaces are locally convex. 1 are equipped with the F-norm they are not locally convex, since the only convex neighborhood of zero is the whole space ... an atomless, finite measure μ and 0 < p < 1 are not locally convex ...

### Famous quotes containing the word locally:

To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.
Clifford Geertz (b. 1926)