Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Easy $ S$ and $ L$ groups


Author: J. Roitman
Journal: Proc. Amer. Math. Soc. 78 (1980), 424-428
MSC: Primary 54G20; Secondary 54H13
MathSciNet review: 553388
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [E] R. Engelking, Outline of general topology, Translated from the Polish by K. Sieklucki, North-Holland Publishing Co., Amsterdam; PWN-Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. MR 0230273 (37 #5836)
  • [G] Fred Galvin, Chain conditions and products, Fund. Math. 108 (1980), no. 1, 33–48. MR 585558 (81m:03058)
  • [HJ$ _{1}$] A. Hajnal and I. Juhász, A consistency result concerning hereditarily $ \alpha $-separable spaces, Proc. Bolyai Janos Math. Soc. Coll., Keszthely, 1972.
  • [HJ$ _{2}$] -, On hereditarily $ \alpha $-Lindelöf and $ \alpha $-separable spaces. II, Fund. Math. 91 (1973-74), 147-158.
  • [JKR] I. Juhász, K. Kunen and M. E. Rudin, Another hereditarily separable non-Lindelöf space (to appear).
  • [K] Kenneth Kunen, Strong 𝑆 and 𝐿 spaces under 𝑀𝐴, Set-theoretic topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975-1976) Academic Press, New York, 1977, pp. 265–268. MR 0440487 (55 #13362)
  • [KT] K. Kunen and F. Tall, Between Martin's axiom and Suslin's hypothesis, General Topology and Appl. (to appear).
  • [R$ _{1}$] J. Roitman, The spread of regular spaces (to appear).
  • [R$ _{2}$] -, Adding a random or a Cohen real: topological consequences and the effect on Martin's Axiom (to appear).
  • [Z] Phillip Zenor, Hereditary 𝔪-separability and the hereditary 𝔪-Lindelöf property in product spaces and function spaces, Fund. Math. 106 (1980), no. 3, 175–180. MR 584491 (82a:54039)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54G20, 54H13

Retrieve articles in all journals with MSC: 54G20, 54H13


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0553388-2
PII: S 0002-9939(1980)0553388-2
Article copyright: © Copyright 1980 American Mathematical Society