Concerning Menger regular curves

Concerning Simple Continuous Curves

Various definitions of simple continuous arcs and closed curves have been given, f The definitions of arcs usually contain the requirement that the point-set in question should be bounded. In attempting to prove that every interval t of an open curve as defined in a recent paper \ is a simple continuous arc, while I found it easy to prove that t satisfies all the other requirements of Janiszews...

Concerning Connected and Regular Point Sets

In this paper an extension will be given of a theorem of the author'sf which states that if A and B are any two points of a continuous curve M, and K denotes the set of all those points of M which separate} A and B in M, then K+A+B is a closed set of points. I t will be shown that if A and B are any two points of any connected and regular (connected im kleinen) point set M, and K denotes the se...

A Note concerning Completely Regular Gyspaces1

Two results concerning distance-regular directed graphs

The study of distance-regular directed graphs can be reduced to that of short distance-regular directed graphs. We consider the eigenspaces of the intersection matrix of a short distance-regular directed graph and show that nearly all the eigenvalues are nonreal. Next we show that a nontrivial short distance-regular directed graph is primitive.

On Two Conjectures concerning Convex Curves

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 RP . Namely, we show that i) the tangent developable of any convex curve in RP 3 has degree 4 and ii) construct an example of 4 tangent lines to a convex curve in RP 3 such that no real line intersects all four of them....