Coordinate rings of topological Klingenberg planes I: The affine perspective |
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Authors: | C. A. Baker J. W. Lorimer |
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Affiliation: | (1) Department of Mathematics and Computer Science, Mount Allison University, EOA 3CO Sackville, New Brunswick, Canada;(2) Department of Mathematics, University of Toronto, M5S 1A1 Toronto, Ontario, Canada |
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Abstract: | Although the coordinate ternary field of a topological affine plane is topological, the converse does not hold. However, an affine plane is topological precisely when its coordinate biternary fields are topological. We extend this result to topological biternary rings and their topological affine Klingenberg planes. Then we examine the locally compact situation. Finally, following the ideas of Knarr and Weigand, we show that in certain circumstances, the continuity of the ternary operators is sufficient to ensure that the biternary ring is topological. This facilitates the construction of locally compact, locally connected affine Klingenberg planes.Dedicated to Professor Dr. Helmut Salzmann on his 65th birthday |
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Keywords: | 51E15 54H13 |
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