### Some articles on *locally convex, convex*:

Discontinuous Linear Map - Beyond Normed Spaces

... but there exist infinite dimensional

... 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

... Call a metric space X

**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)

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