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POINT-FREE GEOMETRY, OVALS, AND HALF-PLANES

  • GIANGIACOMO GERLA (a1) and RAFAŁ GRUSZCZYŃSKI (a2)
Abstract

In this paper we develop a point-free system of geometry based on the notions of region, parthood, and ovality, the last one being a region-based counterpart of the notion of convex set. In order to show that the system we propose is sufficient to reconstruct an affine geometry we make use of a theory of a Polish mathematician Aleksander Śniatycki from [15], in which the concept of half-plane is assumed as basic.

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Corresponding author
*THE INTERNATIONAL INSTITUTE FOR ADVANCED SCIENTIFIC STUDIES (IIASS) SALERNO, ITALY E-mail: ggerla104@gmail.com URL: www.ggerla.it
DEPARTMENT OF LOGIC NICOLAUS COPERNICUS UNIVERSITY IN TORUŃ POLAND E-mail: gruszka@umk.pl URL: www.umk.pl/∼gruszka
References
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