Separability, the countable chain condition and the Lindelöf property in linearly orderable spaces

Separability, the countable chain condition and the Lindelöf property in linearly orderable spaces
HTML articles powered by AMS MathViewer

by D. J. Lutzer and H. R. Bennett PDF

Proc. Amer. Math. Soc. 23 (1969), 664-667 Request permission

References

A. V. Arhangel′skiĭ, Mappings and spaces, Russian Math. Surveys 21 (1966), no. 4, 115–162. MR 0227950, DOI 10.1070/RM1966v021n04ABEH004169

Quasi-developable spaces

Garrett Birkhoff, Lattice theory, American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1961. Revised ed. MR 0123490
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
Takeshi Inagaki, Les espaces abstraits et les ensembles ordonnés, J. Fac. Sci. Hokkaido Imp. Univ. Ser. I. 8 (1940), 145–162 (French). MR 0001816
Takeshi Inagaki, Les espaces abstraits et les ensembles ordonnés, J. Fac. Sci. Hokkaido Imp. Univ. Ser. I. 8 (1940), 145–162 (French). MR 0001816
F. B. Jones, Concerning certain linear abstract spaces and simple continuous curves, Bull. Amer. Math. Soc. 45 (1939), 623–628. MR 268, DOI 10.1090/S0002-9904-1939-07054-7
John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
Georges Kurepa, Le problème de Souslin et les espaces abstraits, Rev. Ci. (Lima) 47 (1945), 457–488 (French). MR 15449

Consistency of the generalized Souslin hypothesis

14

David J. Lutzer, A metrization theorem for linearly orderable spaces, Proc. Amer. Math. Soc. 22 (1969), 557–558. MR 248761, DOI 10.1090/S0002-9939-1969-0248761-1
V. I. Ponomarev, The metrizability of a finally compact $p$-space with pointwise countable basis, Dokl. Akad. Nauk SSSR 174 (1967), 1274–1277 (Russian). MR 0216465
Mary Ellen Rudin, Countable paracompactness and Souslin’s problem, Canadian J. Math. 7 (1955), 543–547. MR 73155, DOI 10.4153/CJM-1955-058-8
Ladislav Skula, Hereditary $m$-separability of an ordered space, C̆asopis Pěst. Mat. 90 (1965), 451–454 (Czech, with Russian and English summaries). MR 0187193
S. Tennenbaum, Souslin’s problem, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 60–63. MR 224456, DOI 10.1073/pnas.59.1.60