Easy $S$ and $L$ groups
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- by J. Roitman PDF
- Proc. Amer. Math. Soc. 78 (1980), 424-428 Request permission
Abstract:
We give a simple proof that the existence of strong S or L spaces implies the existence of strong S or L groups; in fact the algebraic structure can be varied quite a bit. We also construct, under CH, S and L groups whose squares are neither S nor L.References
- R. Engelking, Outline of general topology, North-Holland Publishing Co., Amsterdam; PWN—Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. Translated from the Polish by K. Sieklucki. MR 0230273
- Fred Galvin, Chain conditions and products, Fund. Math. 108 (1980), no. 1, 33–48. MR 585558, DOI 10.4064/fm-108-1-33-48 A. Hajnal and I. Juhász, A consistency result concerning hereditarily $\alpha$-separable spaces, Proc. Bolyai Janos Math. Soc. Coll., Keszthely, 1972. —, On hereditarily $\alpha$-Lindelöf and $\alpha$-separable spaces. II, Fund. Math. 91 (1973-74), 147-158. I. Juhász, K. Kunen and M. E. Rudin, Another hereditarily separable non-Lindelöf space (to appear).
- Kenneth Kunen, Strong $S$ and $L$ spaces under $MA$, Set-theoretic topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975–1976) Academic Press, New York, 1977, pp. 265–268. MR 0440487 K. Kunen and F. Tall, Between Martin’s axiom and Suslin’s hypothesis, General Topology and Appl. (to appear). J. Roitman, The spread of regular spaces (to appear). —, Adding a random or a Cohen real: topological consequences and the effect on Martin’s Axiom (to appear).
- Phillip Zenor, Hereditary ${\mathfrak {m}}$-separability and the hereditary ${\mathfrak {m}}$-Lindelöf property in product spaces and function spaces, Fund. Math. 106 (1980), no. 3, 175–180. MR 584491, DOI 10.4064/fm-106-3-175-180
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 424-428
- MSC: Primary 54G20; Secondary 54H13
- DOI: https://doi.org/10.1090/S0002-9939-1980-0553388-2
- MathSciNet review: 553388