Previous |  Up |  Next

Article

Title: Variations of uniform completeness related to realcompactness (English)
Author: Hušek, Miroslav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 58
Issue: 4
Year: 2017
Pages: 501-518
Summary lang: English
.
Category: math
.
Summary: Various characterizations of realcompactness are transferred to uniform spaces giving non-equivalent concepts. Their properties, relations and characterizations are described in this paper. A Shirota-like characterization of certain uniform realcompactness proved by Garrido and Meroño for metrizable spaces is generalized to uniform spaces. The paper may be considered as a unifying survey of known results with some new results added. (English)
Keyword: realcompactness
Keyword: realcompleteness
Keyword: uniform space
MSC: 54D60
MSC: 54E15
idZBL: Zbl 06837082
idMR: MR3737121
DOI: 10.14712/1213-7243.2015.225
.
Date available: 2017-12-12T06:52:30Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/146993
.
Reference: [1] Chekeev A.A.: Uniformities for Wallman compactifications and realcompactifications.Topology Appl. 201 (2016), 145–156. Zbl 1342.54021, MR 3461161, 10.1016/j.topol.2015.12.033
Reference: [2] Chekeev A.A., Kasymova T.J.: Ultrafilter-completeness on zero-sets of uniformly continuous functions.submitted to Proceedings Prague Toposym, 2016.
Reference: [3] Engelking R.: General Topology.Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321
Reference: [4] Frolík Z.: A generalization of realcompact spaces.Czechoslovak Math. J. 13 (1963), 127–137. Zbl 0112.37603, MR 0155289
Reference: [5] Garrido M.I., Meroño A.S.: New types of completeness in metric spaces.Ann. Acad. Sci. Fenn. Math. 39 (2014), 733–758. Zbl 1303.54010, MR 3237048, 10.5186/aasfm.2014.3934
Reference: [6] Garrido M.I., Meroño A.S.: The Samuel realcompactification.Abstracts of Prague Toposym, 2016.
Reference: [7] Garrido M.I., Meroño A.S.: The Samuel realcompactification.submitted to Proceedings Prague Toposym, 2016. MR 3688464
Reference: [8] Gillman L.: Real-compact spaces (Q-spaces).Bull. Amer. Math. Soc. 63 (1957), 144–145.
Reference: [9] Gillman L., Jerison M.: Rings of Continuous Functions.Van Nostrand Co., Princeton, NJ-Toronto-London-New York, 1960. Zbl 0327.46040, MR 0116199
Reference: [10] Hejcman J.: Boundedness in uniform spaces and topological groups.Czechoslovak Math. J. 9 (1959), 544–563. Zbl 0132.18202, MR 0141075
Reference: [11] Hejcman J.: On conservative uniform spaces.Comment. Math. Univ. Carolin. 7 (1966), 411–417. Zbl 0181.50902, MR 0202107
Reference: [12] Herrlich H.: Fortsetzbarkeit stetiger Abbildungenand Kompaktheitsgrad topologischer Räume.Math. Z. 96 (1967), 64–72. MR 0208560, 10.1007/BF01111452
Reference: [13] Hewitt E.: Rings of real-valued continuous functions, I.Trans. Amer. Math. Soc. 64 (1948), 45–99. Zbl 0032.28603, MR 0026239, 10.1090/S0002-9947-1948-0026239-9
Reference: [14] Hušek M.: The class of k-compact spaces is simple.Math. Z. 110 (1969), 123–126. Zbl 0175.49601, MR 0244947, 10.1007/BF01124977
Reference: [15] Hušek M., Pulgarín A.: Banach-Stone-like theorems for lattices of uniformly continuous functions.Quaest. Math. 35 (2012), 417–430. Zbl 1274.54059, MR 2999998, 10.2989/16073606.2012.742238
Reference: [16] Hušek M., Pulgarín A.: When lattices of uniformly continuous functions on $X$ determine $X$.Topology Appl. 194 (2015), 228–240. Zbl 1328.54013, MR 3404615
Reference: [17] Isbell J.R.: Euclidean and weak uniformities.Pacific J. Math. 8 (1958), 67–86. Zbl 0081.16802, MR 0097794, 10.2140/pjm.1958.8.67
Reference: [18] Isbell J.R.: Algebras of uniformly continuous functions.Ann. of Math. 68 (1958), 96–125. Zbl 0081.11101, MR 0103407, 10.2307/1970045
Reference: [19] Isbell J.R.: Uniform Spaces.Math. Surveys, 12, American Mathematical Society, Rhode Island, 1964. Zbl 0124.15601, MR 0170323
Reference: [20] Katětov M.: On real-valued functions on topological spaces.Fund. Math. 38 (1951), 85–91. MR 0050264, 10.4064/fm-38-1-85-91
Reference: [21] Mrówka S.: Some properties of Q-spaces.Bull. Acad. Polon. Sci. Ser. Math. 5 (1957), 947–950. Zbl 0079.38602, MR 0095465
Reference: [22] Mrówka S.: An elementary proof of Katětov's theorem concerning Q-spaces.Michigan Math. J. 11 (1964), 61–63. Zbl 0117.16002, MR 0161308, 10.1307/mmj/1028999035
Reference: [23] Nachbin L.: Topological vector spaces of continuous functions.Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 471–474. Zbl 0055.09803, MR 0063647, 10.1073/pnas.40.6.471
Reference: [24] Njastad O.: On real-valued proximity mappings.Math. Ann. 154 (1964), 413–419. Zbl 0121.39401, MR 0166757, 10.1007/BF01375524
Reference: [25] Pelant J.: Reflections not preserving completeness.Seminar Uniform Spaces (Prague 1973–1974), pp. 235–240. Zbl 0327.54024, MR 0474219
Reference: [26] Rice M.D., Reynolds G.D.: Completeness and covering properties of uniform spaces.Quart. J. Math. Oxford 29 (1978), 367–374. Zbl 0411.54028, MR 0509702, 10.1093/qmath/29.3.367
Reference: [27] Rice M.D.: Subcategories of uniform spaces.Trans. Amer. Math. Soc. 201 (1975), 305–314. Zbl 0615.54019, MR 0358708, 10.1090/S0002-9947-1975-0358708-2
Reference: [28] Shirota T.: On spaces with a complete structure.Proc. Japan Acad. 27 (1951), 513–516. Zbl 0045.25702, MR 0048781
Reference: [29] Shirota T.: A class of topological spaces.Osaka Math. J. 4 (1952), 23–40. Zbl 0047.41704, MR 0050872
Reference: [30] Weir M.D.: Hewitt-Nachbin Spaces.North Holland, Amsterdam, 1975. Zbl 0314.54002, MR 0514909
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_58-2017-4_8.pdf 334.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo