On Locally Convex Curves

Some Results on Boundedness in Locally Convex Cones

On Locally Simple Curves

Since q<3n~*, the expression in the parenthesis is positive for n large enough, and ]C*-i|/(**)| < 2 n , unless <z = 0. But g = 0 means that every s„= — 1, and f(z) = (z+l). The theorem has thus been proved for large values of n. (5) For small values of n the theorem is incorrect. For example, if/(s) = (2+1) • ( 2 1 / 2 ) , then \f(e) | has relative extrema for 0 = 0, TT, arc cos (1/8), and the...

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Two Conjectures on Convex Curves

Department of Mathematics, University of Oil and Gas (Gubkin) Moscow 117036, Russia [email protected] Department of Mathematics, University of Stockholm S-10691, Sweden, [email protected] Abstra t. In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP3. Namely...