POINT-FREE GEOMETRY, OVALS, AND HALF-PLANES

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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