×

Uncountable powers of R can be almost Lindelöf. (English) Zbl 0396.54015


MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54C50 Topology of special sets defined by functions
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
28A10 Real- or complex-valued set functions

References:

[1] FREMLIN, D.H.: Topological Riesz Spaces and Measure Theory. Cambridge: University Press 1974. · Zbl 0273.46035
[2] FREMLIN, D.H., GARLING, D.J.H., HAYDON, R.G.: Bounded measures on topological spaces. Proc. London Math. Soc. (3)25, 115-136 (1972). · Zbl 0236.46025 · doi:10.1112/plms/s3-25.1.115
[3] HECHLER, S.H.: On \[ \(\backslash\)underset\{\(\backslash\)raise0.3em\(\backslash\)hbox\{\(\smash{\scriptscriptstyle\thicksim}\)\}\}\{N\} \^\{\(\backslash\)aleph \_1 \} \] and the almost-Lindelöf property. Proc. Amer. Math. Soc.52, 353-355 (1975).
[4] KEMPERMAN, J.H.B., MAHARAM, D.: \[ \(\backslash\)underset\{\(\backslash\)raise0.3em\(\backslash\)hbox\{\(\smash{\scriptscriptstyle\thicksim}\)\}\}\{R\} \^\(\backslash\)mathbb\{C\} \] is not almost Lindelöf. Proc. Amer. Math. Soc.24, 772-773 (1970).
[5] MARTIN, D.A., SOLOVAY, R.M.: Internal Cohen extensions. Ann. Math. Logic2, 143-178 (1970). · Zbl 0222.02075 · doi:10.1016/0003-4843(70)90009-4
[6] MORAN, W.: The additivity of measures on completely regular spaces. J. London Math. Soc.43, 633-639 (1968). · Zbl 0159.07802 · doi:10.1112/jlms/s1-43.1.633
[7] ROSS, K.A., STONE, A.H.: Products of separable spaces. Amer. Math. Monthly71, 393-403 (1964). · Zbl 0119.38202 · doi:10.2307/2313241
[8] RUDIN, M.E.: Martin’s Axiom. Chapter B6 of Handbook of Mathematical Logic, ed. J.Barwise. North-Holland 1977.
[9] SCHWARTZ, L.: Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures. Oxford: University Press 1973. · Zbl 0298.28001
[10] SOLOVAY, R., TENNENBAUM, S.: Iterated Cohen extensions and Souslin’s problem. Ann. of Math. (2)94, 201-245 (1971). · Zbl 0244.02023 · doi:10.2307/1970860
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.