Abstract
We show that a pointwise convergent sequence (σ n) n∈N of continuous collineations of a compact projective plane converges uniformly if and only if the pointwise limitα of (σ n) n∈N has a quadrangle in its image. Moreoverα is then a continuous collineation. Furthermore, we derive that a homomorphism between topological projective planes is continuous if and only if it is continuous at some point.
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Kummetz, R. Convergence of automorphisms of compact projective planes. J Geom 66, 136–143 (1999). https://doi.org/10.1007/BF01225677
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DOI: https://doi.org/10.1007/BF01225677