Bulletin of the American Mathematical Society

MathSciNet review: 1567286
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: J. M. van Wouwe
Title: $GO$-spaces and generalizations of metrizability
Additional book information: Mathematical Centre Tracts, Volume 104, Mathematisch Centrum, Amsterdam, The Netherlands, 1979, x + 117 pp.

[A] A. Arhangel'skiĭ, On a class of spaces containing all metric and all locally compact spaces, Soviet Math. Dokl. 4 (1963), 1051-1055.

K. Alster, Subparacompactness in Cartesian products of generalized ordered topological spaces, Fund. Math. 87 (1975), 7–28. MR 451210, DOI 10.4064/fm-87-1-7-28

B. J. Ball, Countable paracompactness in linearly ordered spaces, Proc. Amer. Math. Soc. 5 (1954), 190–192. MR 62419, DOI 10.1090/S0002-9939-1954-0062419-2

Harold R. Bennett, A note on point-countability in linearly ordered spaces, Proc. Amer. Math. Soc. 28 (1971), 598–606. MR 275377, DOI 10.1090/S0002-9939-1971-0275377-2

H. R. Bennett and D. J. Lutzer, Certain hereditary properties and metrizability in generalized ordered spaces, Fund. Math. 107 (1980), no. 1, 71–84. MR 584660, DOI 10.4064/fm-107-1-71-84

[Bi] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ. no. 25, New York, 1940.

Carlos J. R. Borges, On metrizability of topological spaces, Canadian J. Math. 20 (1968), 795–804. MR 231355, DOI 10.4153/CJM-1968-078-1

J. van Dalen and E. Wattel, A topological characterization of ordered spaces, General Topology and Appl. 3 (1973), 347–354. MR 341431

Samuel Eilenberg, Ordered topological spaces, Amer. J. Math. 63 (1941), 39–45. MR 3201, DOI 10.2307/2371274

M. J. Faber, Metrizability in generalized ordered spaces, Mathematical Centre Tracts, No. 53, Mathematisch Centrum, Amsterdam, 1974. MR 0418053

[Fi] V. Filippov, On feathered paracompacta, Soviet Math. Dokl. 9 (1968), 161-164.

Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199

Horst Herrlich, Ordnungsfähigkeit topologischer Räume, Inaugural-Dissertation zur Erlangung der Doktorwürde der Mathematisch-Naturwissenschaftlichen Fakultät der Freien Universität Berlin, Berlin, 1962 (German). MR 0154246

R. W. Heath and D. J. Lutzer, Dugundji extension theorems for linearly ordered spaces, Pacific J. Math. 55 (1974), 419–425. MR 370477

R. W. Heath, D. J. Lutzer, and P. L. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481–493. MR 372826, DOI 10.1090/S0002-9947-1973-0372826-2

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

E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375–376. MR 152985, DOI 10.1090/S0002-9904-1963-10931-3

Ernest A. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math. 23 (1971), 199–214. MR 287502

A. Miščenko, Spaces with a pointwise denumerable basis, Dokl. Akad. Nauk SSSR 144 (1962), 985–988 (Russian). MR 0138090

Kiiti Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365–382. MR 165491, DOI 10.1007/BF01362570

Keiô Nagami, $\Sigma$-spaces, Fund. Math. 65 (1969), 169–192. MR 257963, DOI 10.4064/fm-65-2-169-192

[Ny] P. Nyikos, A compact, nonmetrizable space P such that P (preprint).

Akihiro Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 9 (1968), 236–254 (1968). MR 230283

T. Przymusiński, A Lindelöf space $X$ such that $X^{2}$ is normal but not paracompact, Fund. Math. 78 (1973), no. 3, 291–296. MR 321007, DOI 10.4064/fm-78-3-291-296

Mary Ellen Rudin, Interval topology in subsets of totally orderable spaces, Trans. Amer. Math. Soc. 118 (1965), 376–389. MR 179751, DOI 10.1090/S0002-9947-1965-0179751-6

Mary Ellen Rudin, Souslin’s conjecture, Amer. Math. Monthly 76 (1969), 1113–1119. MR 270322, DOI 10.2307/2317183

R. H. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631–632. MR 20770, DOI 10.1090/S0002-9904-1947-08858-3

V. A. Koščeev, Some properties of the $\delta$-projection in normed linear spaces, Izv. Vysš. Učebn. Zaved. Matematika 5(168) (1976), 36–42 (Russian). MR 0487400

[A] A. Arhangel'skiĭ, On a class of spaces containing all metric and all locally compact spaces, Soviet Math. Dokl. 4 (1963), 1051-1055.




[A1] K. Alster, Subparacompactness in cartesian products of generalized ordered spaces, Fund. Math. 87 (1975), 7-28. MR 0451210




[Ba] B. J. Ball, Countable paracompactness in linearly ordered spaces, Proc. Amer. Math. Soc. 5 (1954), 190-192. MR 62419




[Be] H. R. Bennett, Point-countability in ordered spaces, Proc. Amer. Math. Soc. 28 (1971), 598-606. MR 275377




[BeL] H. R. Bennett and D. J. Lutzer, Certain hereditary properties and metrizability in generalized ordered spaces, Fund. Math. (to appear). MR 584660




[Bi] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ. no. 25, New York, 1940.




[Bo] C. J. R. Borges, On metrizability of topological spaces, Canad. J. Math. 20 (1968), 795-804. MR 231355




[vDW] J. van Dalen and E. Wattell, A topological characterization of ordered spaces, General Topology and Appl. 3 (1973), 347-354. MR 341431




[E] S. Eilenberg, Ordered topological spaces, Amer. J. Math. 63 (1941), 39-45. MR 3201




[Fa] M. J. Faber, Metrizability in generalized ordered spaces, Math. Center Tracts, no. 53, Amsterdam, 1974. MR 418053




[Fi] V. Filippov, On feathered paracompacta, Soviet Math. Dokl. 9 (1968), 161-164.




[GJ] L. Gillman and M. Jerison, Rings of continuous functions, van Nostrand, New York, 1960. MR 116199




[H] H. Herrlich, Ornungsfahigkeit topologischer Raume, Inaugural dissertation, Berlin, 1962. MR 154246




[HL] R. W. Heath and D. J. Lutzer, Dugundji extension theorems for linearly ordered spaces. Pacific J. Math. 55 (1974), 419-425. MR 370477




[HLZ] R. W. Heath, D. J. Lutzer and P. L. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481-493. MR 372826




[L] D. J. Lutzer, A metrization theorem for linearly orderable spaces, Proc. Amer. Math. Soc. 22 (1969), 557-558. MR 248761




[Mi₁] E. A. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375-376. MR 152985




[Mi₂] E. A. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math. 23 (1971), 199-214. MR 287502




[Mc] A. Miscenko, Spaces with a pointwise denumerable basis, Soviet Math. Dokl. 3 (1962), 855-858. MR 138090




[Mo] K. Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365-382. MR 165491




[Na] K. Nagami, ∑-spaces, Fund. Math. 65 (1969), 169-192. MR 257963




[Ny] P. Nyikos, A compact, nonmetrizable space P such that P (preprint).




[O] A. Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daiyaku, Sect A 9 (1967), 236-254. MR 230283




[P] T. Przymusiński, A Lindelöf space X such that X, Fund. Math. 78 (1973), 291-296. MR 321007




[R₁] M. E. Rudin, Interval topology in subsets of totally orderable spaces, Trans. Amer. Math. Soc. 118 (1965), 376-389. MR 179751




[R₂] M. E. Rudin, Souslin's conjecture, Amer. Math. Monthly 76 (1969), 1113-1119. MR 270322




[S] R. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631-632. MR 20770




[V] N. V. Veličko, Ordered p-spaces, Izv. Vysš. Učebn Zaved. Matematika 1976, no. 9 (172), 25-36. MR 487400