There are many Kunen compact L-spaces

Brandsma, Henno; van Mill, Jan

doi:10.1090/S0002-9939-99-05186-2

There are many Kunen compact L-spaces
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by Henno Brandsma and Jan van Mill PDF

Proc. Amer. Math. Soc. 128 (2000), 2165-2170 Request permission

Abstract:

We prove that under CH there are $\omega _1$ non-homeomorphic Kunen compact L-spaces. Moreover there exist models of ZFC that have $2^{\omega _1}$ many non-homeomorphic Kunen spaces.

References

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
Henno Brandsma and Jan van Mill, A compact HL-space need not have a monolithic hyperspace, Proc. Amer. Math. Soc. 126 (1998), no. 11, 3407–3411. MR 1452794, DOI 10.1090/S0002-9939-98-04374-3
H. Brandsma and J. van Mill, Every Kunen-like L-space has a non-monolithic hyperspace, Proceedings of the 12th Summer Conference on General Topology and its Applications, 1997.
Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
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
Kenneth Kunen and Jan van Mill, Measures on Corson compact spaces, Fund. Math. 147 (1995), no. 1, 61–72. MR 1330107
E. V. Ščepin, Functors and uncountable degrees of compacta, Uspekhi Mat. Nauk 36 (1981), no. 3(219), 3–62, 255 (Russian). MR 622720
Z. Semadeni, Banach spaces of continuous functions, volume I, Monografie Matematyczne, vol. 55, PWN - Polish scientific publishers, Warsaw, 1971. 45:5730