Bounded tightness for locally convex spaces and spaces C(X)

Asymmetric locally convex spaces

The aim of the present paper is to introduce the asymmetric locally convex spaces and to prove some basic properties. Among these I do mention the analogs of the EidelheitTuckey separation theorems, of the Alaoglu-Bourbaki theorem on the weak compactness of the polar of a neighborhood of 0, and a Krein-Milman-type theorem. These results extend those obtained by Garcı́a-Raffi et al. (2003) and Co...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Seminorms and Locally Convex Spaces

The first point is to describe vector spaces with topologies arising from (separating) families of semi-norms. These all turn out to be locally convex, for straightforward reasons. The second point is to check that any locally convex topological vectorspace's topology can be given by a collection of seminorms. These seminorms are made in a natural way from a local basis consisting of balanced c...

Quasi-barrelled Locally Convex Spaces

1. R. E. Lane, Absolute convergence of continued fractions, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 904-913. 2. R. E. Lane and H. S. Wall, Continued fractions with absolutely convergent even and odd parts, Trans. Amer. Math. Soc. vol. 67 (1949) pp. 368-380. 3. W. T. Scott and H. S. Wall, A convergence theorem for continued fractions, Trans. Amer. Math. Soc. vol. 47 (1940) pp. 155-172. 4. H. S....

Smooth Locally Convex Spaces * 1 )

The main theorem is Let E be a separable (real) Frèchet space with a nonseparable strong dual Then E is not strongly Dp-smooth. It follows that if X is uncountable, locally compact, a-compact, metric space, then C(X) (with the topology of compact convergence) does not have a class of seminorms which generate its topology and are Frechet differentiable (away from their null-spaces). 1. Prelimina...