Topology Proceedings
Document # baak-33
Electronic Version 24 Summer (1999) |
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Universal ultrametric spaces of smallest weight
Jerry E. Vaughan
We modify a construction of A. Lemin and V. Lemin to construct an ultrametric space LW\tau' which is universal (in the sense of isometry) for ultrametric spaces of weight at most \tau. Under the singular cardinal hypothesis, a set-theoretic assumption whose negation is related to large cardinals, the weight of LW\tau' is \tau for all \tau > \mathfrak c. This provides a solution to a problem raised by the Lemins.
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Date published electronically: March 5, 2001.