A non-Hausdorff Ascoli theorem for $k_{3}$-spaces
HTML articles powered by AMS MathViewer
- by Geoffrey Fox and Pedro Morales PDF
- Proc. Amer. Math. Soc. 39 (1973), 633-636 Request permission
Abstract:
The paper establishes an Ascoli theorem in the space of continuous functions on a ${k_3}$-space to a regular space. The theorem, in terms of even continuity and the compact open topology ${\tau _c}$, properly contains the Ascoli theorems of Myers, Gale, Kelley-Morse, Bagley-Yang, and the ${k_3}$-space theorem of Noble.References
- R. W. Bagley and J. S. Yang, On $k$-spaces and function spaces, Proc. Amer. Math. Soc. 17 (1966), 703β705. MR 192468, DOI 10.1090/S0002-9939-1966-0192468-3
- R. Brown, Function spaces and product topologies, Quart. J. Math. Oxford Ser. (2) 15 (1964), 238β250. MR 165497, DOI 10.1093/qmath/15.1.238
- D. E. Cohen, Spaces with weak topology, Quart. J. Math. Oxford Ser. (2) 5 (1954), 77β80. MR 63043, DOI 10.1093/qmath/5.1.77
- Ralph H. Fox, On topologies for function spaces, Bull. Amer. Math. Soc. 51 (1945), 429β432. MR 12224, DOI 10.1090/S0002-9904-1945-08370-0
- David Gale, Compact sets of functions and function rings, Proc. Amer. Math. Soc. 1 (1950), 303β308. MR 36503, DOI 10.1090/S0002-9939-1950-0036503-X
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- S. B. Myers, Equicontinuous sets of mappings, Ann. of Math. (2) 47 (1946), 496β502. MR 17526, DOI 10.2307/1969088
- N. Noble, Ascoli theorems and the exponential map, Trans. Amer. Math. Soc. 143 (1969), 393β411. MR 248727, DOI 10.1090/S0002-9947-1969-0248727-6
- N. Noble, The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187β198. MR 257987, DOI 10.1090/S0002-9947-1970-0257987-5
- Harry Poppe, Stetige Konvergenz und der Satz von Ascoli und ArzelΓ , Math. Nachr. 30 (1965), 87β122 (German). MR 188973, DOI 10.1002/mana.19650300107
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 633-636
- MSC: Primary 54C35
- DOI: https://doi.org/10.1090/S0002-9939-1973-0391004-X
- MathSciNet review: 0391004