Abstract
We study a special class of models of R3-spaces in the sense of Betten. We single out some of the properties of these models, and use these properties as additional axioms for general R3-spaces. Then we investigate the consequences of these new axioms in general R3-spaces. We prove the continuity of the geometric operations which involve planes, and we characterize the planes in incidence geometric terms. Using these results, we study the topology of the space of planes and of line pencils, and we prove the continuity of collineations. The obtained results are applied to our concrete examples.
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Klein, H. Models of topological space geometries. J Geom 59, 77–93 (1997). https://doi.org/10.1007/BF01229567
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DOI: https://doi.org/10.1007/BF01229567