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A Property of Convex Pseudopolyhedra

Published online by Cambridge University Press:  20 November 2018

Z.A. Melzak
Z.A. Melzak*
Affiliation:
McGill University
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In this note we prove one theorem and make a few conjectures, all of which are connected with the following problem raised by S. Mazur [l]: does there exist a closed convex surface whose plane sections give all plane closed convex curves, up to affinities? For our purposes we define a convex pseudopolyhedron to be the closed convex hull of a countable bounded nonplanar sequence of points in E3 with exactly one limit point.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 2 , Issue 1 , 01 January 1959 , pp. 31 - 32
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Ulam, S.M., Mathematical Problems, mimeographed notes, (Los Alamos, 1954).Google Scholar