Properties of Connected Ortho-convex Sets in the Plane

A. M. Dulliev

Kazan National Research Technical University named after A. N. Tupolev

Abstract: Topological properties of connected ortho-convex sets in the plane, i.e., connected sets convex along the horizontal and vertical lines are studied. Several geometric statements concerning the ortho-separation of ortho-convex sets are proved.

Keywords: ortho-convex set, ortho-half-space, ortho-hyperplane, ortho-separation.

UDC: 514

Received: 06.04.2015

DOI: 10.4213/mzm10379

 English version: Mathematical Notes, 2017, 101:3, 443–459

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