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Using prediction
principles to construct ordered continua
Stephen Watson |
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Vol. 125 (1986), No. 1, 251–256
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Abstract |
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In this paper, we show that the elements of a ♢-sequence can be ordered lexicographically to produce an ordered continuum. An application of this idea answers a question of V. Malyhin and others: Is there a compact Hausdorff space in which no two points have equal character? We show that the consistency strength of the existence of such a space lies between that of an inaccessible and a Mahlo cardinal. We show that compactness is essential in this result by constructing, in ZFC, a σ-compact Hausdorff space in which no two points have equal character. |
Mathematical Subject Classification 2000
Primary: 03E35
Secondary: 03E55, 54A35
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Milestones
Received: 21 September 1984
Published: 1 November 1986
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Authors |
| Stephen Watson | |
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