On complete partially ordered sets and compatible topologies |
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| Authors: | Murray Bell John Ginsburg |
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| Institution: | (1) Department of Mathematics, University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada;(2) Department of Mathematics, University of Winnipeg, R3B 2E9 Winnipeg, Manitoba, Canada |
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| Abstract: | We describe two complete partially ordered sets which are the intersection of complete linear orderings but which have no compatible Hausdorff topology. One is two-dimensional, while the second is countable, and leads to an example of a countable, compact, T
1 space with a countable base which is not the continuous image of any compact Hausdorff space. |
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| Keywords: | Primary: 06A23 secondary: 54D30 |
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