@MISC{Kummetz_convergenceof, author = {Ralph Kummetz}, title = {Convergence of Automorphisms of Compact Projective Planes}, year = {} }

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Abstract

Introduction Convergence and continuity properties of homomorphisms play an important role in the theory of topological projective planes. Grundhofer [8] showed that the set \Sigma of all automorphisms of a compact projective plane is a locally compact transformation group with respect to the topology of uniform convergence; for the special case of compact connected projective planes see also Salzmann [21]. With regards to classification, compact connected projective planes have been successfully investigated by studying their automorphism group, see Salzmann, Betten, Grundhofer, Hahl, Lowen, and Stroppel [22] for a detailed exposition. Salzmann [20] proved that if \Pi is a 2-dimensional compact projective plane, then on \Sigma the topology of pointwise convergence coincides with the topology of uniform convergence. He also showed ([19]) that any homomorphism between 2-dimensional compact projective planes is in fact a homeomorphism. Grundhofer [9] characterized the continuity of non-