A compact HL-space need not have a monolithic hyperspace

Brandsma, Henno; van Mill, Jan

doi:10.1090/S0002-9939-98-04374-3

A compact HL-space need not have a monolithic hyperspace
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by Henno Brandsma and Jan van Mill

Proc. Amer. Math. Soc. 126 (1998), 3407-3411

DOI: https://doi.org/10.1090/S0002-9939-98-04374-3

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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’skiĭ’s.

References

A. V. Arkhangel′skiĭ, Topological homogeneity. Topological groups and their continuous images, Uspekhi Mat. Nauk 42 (1987), no. 2(254), 69–105, 287 (Russian). MR 898622
M. Bell, The hyperspace of a compact space. I, Topology Appl. 72 (1996), no. 1, 39–46. MR 1402235, DOI 10.1016/0166-8641(96)00012-0
Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
Kenneth Kunen, A compact $L$-space under CH, Topology Appl. 12 (1981), no. 3, 283–287. MR 623736, DOI 10.1016/0166-8641(81)90006-7
Mirna D amonja and Kenneth Kunen, Measures on compact HS spaces, Fund. Math. 143 (1993), no. 1, 41–54. MR 1234990, DOI 10.4064/fm-143-1-41-54
S. Negrepontis, Banach spaces and topology, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1045–1142. MR 776642