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A compact HL-space need not have a monolithic hyperspace

Author(s): Henno Brandsma; Jan van Mill
Journal: Proc. Amer. Math. Soc. 126 (1998), 3407-3411.
MSC (1991): Primary 54A20, 54B20, 54D30, 54G20
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Abstract: We show that Kunen's example of a compact L-space, constructed under CH, can be modified so that it has a non-monolithic hyperspace. This answers a question of Bell's. This example is also relevant to a question of Arhangel'skii's.

References:

1.: A.V. Arhangel'ski[??]i, Topological Homogeneity. Topological Groups and their Continuous Images, Russian Math. Surveys 42 (1987), no. 2, 83-131.MR 89b:54004
2.: M. Bell, The Hyperspace of a Compact Space I, Topology and its Applications 72 (1996), 39-46.MR 97j:54010
3.: R. Engelking, General Topology, revised and completed ed., Sigma series in pure mathematics, vol. 6, Heldermann Verlag Berlin, 1989.MR 91c:54001
4.: K. Kunen, A Compact L-space under CH, Topology and its Applications 12 (1981), 283-287.MR 82h:54065
5.: K. Kunen and M. D\v{z}amonja, Measures on Compact HS spaces, Fundamenta Mathematicae 143 (1993), 41-54.MR 94h:54047
6.: S. Negrepontis, Banach Spaces and Topology, Handbook of Set-Theoretic Topology (K. Kunen and J.E. Vaughan, eds.), North-Holland, 1984. MR 86i:46018


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