Some examples in topology
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- by S. P. Franklin and M. Rajagopalan PDF
- Trans. Amer. Math. Soc. 155 (1971), 305-314 Request permission
Abstract:
§1 is concerned with variations on the theme of an ordinal compactification of the integers. Several applications are found, yielding, for instance, an example previously known only modulo the continuum hypothesis, and a counter-example to a published assertion. §2 is concerned with zero-one sequences and §3 with spaces built from sequential fans. Of two old problems of Čech, one is solved and one partly solved. Since the sections are more or less independent, each will have its own introduction. Sequential spaces form the connecting thread, although not all the examples are concerned with them.References
- A. V. Arhangel′skiĭ and S. P. Franklin, Ordinal invariants for topological spaces, Michigan Math. J. 15 (1968), 313-320; addendum, ibid. 15 (1968), 506. MR 0240767
- S. P. Franklin, On unique sequential linits, Nieuw Arch. Wisk. (3) 14 (1966), 12–14. MR 192465
- 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
- S. P. Franklin, On two questions of Moore and Mrowka, Proc. Amer. Math. Soc. 21 (1969), 597–599. MR 251696, DOI 10.1090/S0002-9939-1969-0251696-1 —, A homogeneous Hausdorff ${E_0}$-space which isn’t ${E_1}$, General Topology and its Relations to Modern Analysis and Algebra, III, Proc. Kanpur Top. Conf. (to appear).
- 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
- Edwin Hewitt, On two problems of Urysohn, Ann. of Math. (2) 47 (1946), 503–509. MR 17527, DOI 10.2307/1969089
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- Kenneth D. Magill Jr., A note on compactifications, Math. Z. 94 (1966), 322–325. MR 203681, DOI 10.1007/BF01111663
- Louis F. McAuley, Paracompactness and an example due to F. B. Jones, Proc. Amer. Math. Soc. 7 (1956), 1155–1156. MR 82088, DOI 10.1090/S0002-9939-1956-0082088-7 J. Novak, Sur les expaces ($\mathcal {L}$) et sur les produits cartésiens ($\mathcal {L}$), Publ. Fac. Sci. Univ. Masaryk No. 273 (1939). MR 1, 221
- N. Noble, The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187–198. MR 257987, DOI 10.1090/S0002-9947-1970-0257987-5
- I. I. Parovičenko, On a universal bicompactum of weight $\aleph$, Dokl. Akad. Nauk SSSR 150 (1963), 36–39. MR 0150732
- Mary Ellen Rudin, A separable normal nonparacompact space, Proc. Amer. Math. Soc. 7 (1956), 940–941. MR 81631, DOI 10.1090/S0002-9939-1956-0081631-1
- Mary Ellen Rudin, A technique for constructing examples, Proc. Amer. Math. Soc. 16 (1965), 1320–1323. MR 188976, DOI 10.1090/S0002-9939-1965-0188976-0
- M. Shimrat, Embedding in homogeneous spaces, Quart. J. Math. Oxford Ser. (2) 5 (1954), 304–311. MR 68204, DOI 10.1093/qmath/5.1.304
- Paul Urysohn, Über die Mächtigkeit der zusammenhängenden Mengen, Math. Ann. 94 (1925), no. 1, 262–295 (German). MR 1512258, DOI 10.1007/BF01208659
- R. Vaidyanathaswamy, Set topology, Chelsea Publishing Co., New York, 1960. 2nd ed. MR 0115151
- Phillip Zenor, A class of countably paracompact spaces, Proc. Amer. Math. Soc. 24 (1970), 258–262. MR 256349, DOI 10.1090/S0002-9939-1970-0256349-X
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 155 (1971), 305-314
- MSC: Primary 54.20
- DOI: https://doi.org/10.1090/S0002-9947-1971-0283742-7
- MathSciNet review: 0283742