Spread and local properties

Coutant, Basil

doi:10.1090/S0002-9939-1991-1045132-7

Spread and local properties
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by Basil Coutant

Proc. Amer. Math. Soc. 112 (1991), 893-898

DOI: https://doi.org/10.1090/S0002-9939-1991-1045132-7

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Abstract:

A technique for combining the spread of a space and several local properties is exploited to obtain decompositions of a space and cardinal function bounds on the size and weight. It is shown that a locally countable set is the union of ${\omega _1}$ discrete sets and that under $MA\left ( {{\omega _1}} \right )$ the weight of a manifold is equal to its spread.

References

Martin’s axiom and first-countable

- and

-spaces

Zoltán T. Balogh, Locally nice spaces under Martin’s axiom, Comment. Math. Univ. Carolin. 24 (1983), no. 1, 63–87. MR 703926
Basil Coutant, Some cardinal function relationships between $C_p(X)$ and finite powers of a space $X$, Topology Appl. 39 (1991), no. 3, 245–259. MR 1110568, DOI 10.1016/0166-8641(91)90117-5
Ryszard Engelking, Topologia ogólna, Biblioteka Matematyczna [Mathematics Library], vol. 47, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1975 (Polish). MR 0500779
D. H. Fremlin, Perfect pre-images of $\omega _i$ and the PFA, Topology Appl. 29 (1988), no. 2, 151–166. MR 949366, DOI 10.1016/0166-8641(88)90072-7
R. Hodel, Cardinal functions. I, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1–61. MR 776620
I. Juhász, K. Kunen, and M. E. Rudin, Two more hereditarily separable non-Lindelöf spaces, Canadian J. Math. 28 (1976), no. 5, 998–1005. MR 428245, DOI 10.4153/CJM-1976-098-8
Peter Nyikos, The theory of nonmetrizable manifolds, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 633–684. MR 776633
Judy Roitman, Basic $S$ and $L$, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 295–326. MR 776626