Article

 Title: Locally realcompact and HN-complete spaces (English) Author: Buhagiar, David Author: Chetcuti, Emmanuel Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 48 Issue: 1 Year: 2007 Pages: 107-117 . Category: math . Summary: Two classes of spaces are studied, namely locally realcompact spaces and HN-complete spaces, where the latter class is introduced in the paper. Both of these classes are superclasses of the class of realcompact spaces. Invariance with respect to subspaces and products of these spaces are investigated. It is shown that these two classes can be characterized by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non empty support. It is known that a space is locally realcompact if and only if it is open in its Hewitt-Nachbin realcompactification; we give an external characterization of HN-completeness with respect to the Hewitt-Nachbin realcompactification. In addition, a complete characterization of products of these classes is given. (English) Keyword: Baire measure Keyword: realcompactness Keyword: local realcompactness Keyword: HN-completeness MSC: 28C15 MSC: 54D45 MSC: 54D60 MSC: 54D99 idZBL: Zbl 1199.54157 idMR: MR2338833 . Date available: 2009-05-05T17:01:38Z Last updated: 2012-05-01 Stable URL: http://hdl.handle.net/10338.dmlcz/119642 . Reference: [1] Arhangelskiĭ A.V.: On topological spaces which are complete in the sense of Čech.Vestnik Moskov. Univ. Ser. I Mat. Meh. (1961), 2 37-40 (Russian). MR 0131258 Reference: [2] Blair R.L., van Douwen E.: Nearly realcompact spaces.Topology Appl. 47 3 (1992), 209-221. Zbl 0772.54021, MR 1192310 Reference: [3] Buhagiar D., Chetcuti E., Dvurečenskij A.: Measure-theoretic characterizations of certain topological properties.Bull. Pol. Acad. Sci. 53 1 (2005), 99-109. Zbl 1113.28012, MR 2162757 Reference: [4] Čech E.: On bicompact spaces.Ann. Math. 38 (1937), 823-844. MR 1503374 Reference: [5] Dijkstra J.J.: Measures in topology.Master Thesis, Univ. of Amsterdam, 1977. Reference: [6] Dykes N.: Generalizations of realcompact spaces.Pacific J. Math. 33 (1970), 571-581. Zbl 0197.19201, MR 0276928 Reference: [7] Engelking R.: General Topology.Heldermann, Berlin, 1989 (revised edition). Zbl 0684.54001, MR 1039321 Reference: [8] Frolík Z.: Generalizations of the $G_\delta$-property of complete metric spaces.Czechoslovak Math. J. 10 (1960), 359-379. MR 0116305 Reference: [9] Frolík Z.: A generalization of realcompact spaces.Czechoslovak Math. J. 13 (1963), 127-138. MR 0155289 Reference: [10] Gardner R.J., Pfeffer W.F.: Borel Measures.in: Handbook of Set-Theoretic Topology, Elsevier, 1984, pp.961-1043. Zbl 0593.28016, MR 0776641 Reference: [11] Gillman L., Jerison M.: Rings of Continuous Functions.Springer, New York, 1976. Zbl 0327.46040, MR 0407579 Reference: [12] Hart K.P., Nagata J., Vaughan J.E. (Eds.): Encyclopedia of General Topology.Elsevier Science Publishers B.V., Amsterdam, The Netherlands, 2004. Zbl 1059.54001, MR 2049453 Reference: [13] Hewitt E.: Linear functionals on spaces of continuous functions.Fund. Math. 37 (1950), 161-189. Zbl 0040.06401, MR 0042684 Reference: [14] Isiwata T.: On locally Q-complete spaces, I, II, and III.Proc. Japan Acad. 35 (1959), 232-236, 263-267, 431-434. MR 0107220 Reference: [15] Mack J., Rayburn M., Woods G.: Lattices of topological extensions.Trans. Amer. Math. Soc. 189 (1972), 163-174. MR 0350700 Reference: [16] Nagata J.: Modern General Topology.Elsevier Science Publishers B.V., Amsterdam, The Netherlands, 1985, Second revised edition. Zbl 0598.54001 Reference: [17] Rice M.D., Reynolds G.D.: Weakly Borel-complete topological spaces.Fund. Math. 105 (1980), 179-185. Zbl 0435.54033, MR 0580580 Reference: [18] Sakai M.: A new class of isocompact spaces and related results.Pacific J. Math. 122 1 (1986), 211-221. Zbl 0592.54025, MR 0825232 Reference: [19] Weir M.: Hewitt-Nachbin Spaces.North Holland Math. Studies, American Elsevier, New York, 1975. Zbl 0314.54002, MR 0514909 .

Files

Files Size Format View
CommentatMathUnivCarolRetro_48-2007-1_9.pdf 240.2Kb application/pdf View/Open

Partner of