A Moore space with a $\sigma$-discrete $\pi$-base which cannot be densely embedded in any Moore space with the Baire property
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- by David L. Fearnley PDF
- Proc. Amer. Math. Soc. 127 (1999), 3095-3100 Request permission
Abstract:
The author answers a question raised in the literature about twenty five years ago and raised again more recently in Open Problems in Topology, by G. M. Reed, concerning the conjecture that every Moore space with a $\sigma$-discrete $\pi$-base can be densely embedded in a Moore space having the Baire property. Even though closely related results have made this conjecture seem likely to be true, the author shows that, surprisingly, the conjecture is false.References
- J. M. Aarts and D. J. Lutzer, Pseudo-completeness and the product of Baire spaces, Pacific J. Math. 48 (1973), 1–10. MR 326666, DOI 10.2140/pjm.1973.48.1
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- Ben Fitzpatrick Jr., On dense subsets of Moore spaces. II, Fund. Math. 61 (1967), 91–92. MR 219036, DOI 10.4064/fm-61-1-91-92
- G. M. Reed, Concerning completable Moore spaces, Proc. Amer. Math. Soc. 36 (1972), 591–596. MR 309074, DOI 10.1090/S0002-9939-1972-0309074-2
- G. M. Reed, Lecture notes in mathematics, vol. 378, Springer-Verlag, 1972, pp. 368–384.
- Jan van Mill and George M. Reed (eds.), Open problems in topology, North-Holland Publishing Co., Amsterdam, 1990. MR 1078636
- Kenneth E. Whipple, Cauchy sequences in Moore spaces, Pacific J. Math. 18 (1966), 191–199. MR 196703, DOI 10.2140/pjm.1966.18.191
- H. E. White Jr., First countable spaces that have special pseudo-bases, Canad. Math. Bull. 21 (1978), no. 1, 103–112. MR 482615, DOI 10.4153/CMB-1978-016-5
- J. N. Younglove, Concerning dense metric subspaces of certain non-metric spaces, Fund. Math. 48 (1959), 15–25. MR 111011, DOI 10.4064/fm-48-1-15-25
Additional Information
- David L. Fearnley
- Affiliation: Mathematics Institute, 24-29 St. Giles, Oxford University, Oxford OX1 3LB, England
- Address at time of publication: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- Email: david.fearnley@st-edmund-hall.oxford.ac.uk, davidf@math.byu.edu
- Received by editor(s): June 23, 1997
- Received by editor(s) in revised form: December 12, 1997
- Published electronically: April 23, 1999
- Additional Notes: This material is based on work supported under a National Science Foundation Graduate Fellowship
- Communicated by: Alan Dow
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3095-3100
- MSC (1991): Primary 54D20, 54D25; Secondary 54E52
- DOI: https://doi.org/10.1090/S0002-9939-99-04876-5
- MathSciNet review: 1605960