Symmetrizable and related spaces

Symmetrizable and related spaces
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by Peter W. Harley and R. M. Stephenson PDF

Trans. Amer. Math. Soc. 219 (1976), 89-111 Request permission

A study is made of a family of spaces which contains the symmetrizable spaces as well as many of the well-known examples of perfectly normal spaces.

References

Richard Arens, Note on convergence in topology, Math. Mag. 23 (1950), 229–234. MR 37500, DOI 10.2307/3028991
A. V. Arhangel′skiĭ, Mappings and spaces, Russian Math. Surveys 21 (1966), no. 4, 115–162. MR 0227950, DOI 10.1070/RM1966v021n04ABEH004169

Works in topology and other fields of mathematics

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Linear s-spaces

Dennis A. Bonnett, A symmetrizable space that is not perfect, Proc. Amer. Math. Soc. 34 (1972), 560–564. MR 295275, DOI 10.1090/S0002-9939-1972-0295275-9
P. W. Harley III and G. D. Faulkner, Metrization of symmetric spaces, Canadian J. Math. 27 (1975), no. 5, 986–990. MR 413055, DOI 10.4153/CJM-1975-102-x
V. V. Filippov, Perfectly normal bicompacta, Dokl. Akad. Nauk SSSR 189 (1969), 736–739 (Russian). MR 0256350
S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–115. MR 180954, DOI 10.4064/fm-57-1-107-115
S. P. Franklin, Spaces in which sequences suffice. II, Fund. Math. 61 (1967), 51–56. MR 222832, DOI 10.4064/fm-61-1-51-56
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, DOI 10.1007/978-1-4615-7819-2

Topologies determined by classes of nets

John Wm. Green, Moore-closed spaces, completeness and centered bases, General Topology and Appl. 4 (1974), 297–313. MR 365502, DOI 10.1016/0016-660X(74)90009-9

Semi-metric spaces and related spaces

Robert W. Heath and Ernest A. Michael, A property of the Sorgenfrey line, Compositio Math. 23 (1971), 185–188. MR 287515
F. B. Jones, Concerning normal and completely normal spaces, Bull. Amer. Math. Soc. 43 (1937), no. 10, 671–677. MR 1563615, DOI 10.1090/S0002-9904-1937-06622-5
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
Ernest Michael, Local compactness and Cartesian products of quotient maps and $k$-spaces, Ann. Inst. Fourier (Grenoble) 18 (1968), no. fasc. 2, 281–286 vii (1969) (English, with French summary). MR 244943, DOI 10.5802/aif.300
S. Nedev, Symmetrizable spaces and final compactness, Dokl. Akad. Nauk SSSR 175 (1967), 532–534 (Russian). MR 0216460
V. Niemytzki, Über die Axiome des metrischen Raumes, Math. Ann. 104 (1931), no. 1, 666–671 (German). MR 1512692, DOI 10.1007/BF01457963

Sur les espaces

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et sur les produits cartésiens

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A. J. Ostaszewski, On countably compact, perfectly normal spaces, J. London Math. Soc. (2) 14 (1976), no. 3, 505–516. MR 438292, DOI 10.1112/jlms/s2-14.3.505
R. M. Stephenson Jr., Discrete subsets of perfectly normal spaces, Proc. Amer. Math. Soc. 34 (1972), 605–608. MR 296885, DOI 10.1090/S0002-9939-1972-0296885-5

An alternative to the continuum hypothesis and its uses in general topology

J. E. Vaughan, Classroom Notes: Lexicographic Products and Perfectly Normal Spaces, Amer. Math. Monthly 78 (1971), no. 5, 533–536. MR 1536336, DOI 10.2307/2317766

Countably compact, perfectly normal spaces may or may not be compact

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