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Title: The sup = max problem for the extent of generalized metric spaces (English)
Author: Hirata, Yasushi
Author: Yajima, Yukinobu
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 54
Issue: 2
Year: 2013
Pages: 245-257
Summary lang: English
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Category: math
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Summary: It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces. (English)
Keyword: extent
Keyword: Lindelöf degree
Keyword: $\Sigma$-space
Keyword: strict $p$-space
Keyword: semi-stratifiable
MSC: 03E10
MSC: 54A25
MSC: 54D20
MSC: 54E18
idZBL: Zbl 06221266
idMR: MR3067707
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Date available: 2013-06-25T12:53:25Z
Last updated: 2015-07-06
Stable URL: http://hdl.handle.net/10338.dmlcz/143273
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Reference: [1] Aull C.E.: A generalization of a theorem of Aquaro.Bull. Austral. Math. Soc. 9 (1973), 105–108. Zbl 0255.54015, MR 0372817, 10.1017/S0004972700042933
Reference: [2] Burke D.K.: On $p$-spaces and $w\Delta$-spaces.Pacific J. Math. 35 (1970), 285–296. Zbl 0204.55703, MR 0278255, 10.2140/pjm.1970.35.285
Reference: [3] Creed G.D.: Concerning semi-stratifiable spaces.Pacific J. Math. 32 (1970), 47–54. MR 0254799, 10.2140/pjm.1970.32.47
Reference: [4] Gruenhage G.: Generalized metric spaces.Handbook of Set-theoretic Topology (K. Kunen and J.E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 423–501. Zbl 0794.54034, MR 0776629
Reference: [5] Hajnal A., Juhász I.: Discrete subspaces of topological spaces II.Indag. Math. 31 (1969), 18–30. Zbl 0169.53901, MR 0264585, 10.1016/1385-7258(69)90022-5
Reference: [6] Hajnal A., Juhász I.: Some remarks on a property of topological cardinal functions.Acta Math. Acad. Sci. Hungar. 20 (1969), 25–37. Zbl 0184.26401, MR 0242103, 10.1007/BF01894566
Reference: [7] Jiang S.: Every strict p-space is $\theta $-refinable.Topology Proc. 11 (1986), 309–316. Zbl 0637.54024, MR 0945506
Reference: [8] Jones F.B.: Concering normal and completely normal spaces.Bull. Amer. Math. Soc. 43 (1937), 671–677. MR 1563615, 10.1090/S0002-9904-1937-06622-5
Reference: [9] Juhász I.: Cardinal Functions in Topology.Mathematisch Centrum, Amsterdam, 1971. MR 0340021
Reference: [10] Juhász I.: Cardinal Functions in Topology – Ten Years Later.Mathematisch Centrum, Amsterdam, 1980. Zbl 0479.54001, MR 0576927
Reference: [11] Kunen K., Roitman J.: Attaining the spread at cardinals of cofinality $\omega $.Pacific J. Math. 70 (1977), 199–205. Zbl 0375.54004, MR 0462949, 10.2140/pjm.1977.70.199
Reference: [12] Nagami K.: $\varSigma$-spaces.Fund. Math. 65 (1969), 169–192. MR 0257963
Reference: [13] Okuyama A.: On a generalization of $\varSigma$-spaces.Pacific J. Math 42 (1972), 485–495. MR 0313995, 10.2140/pjm.1972.42.485
Reference: [14] Roitman J.: The spread of regular spaces.General Topology and Appl. 8 (1978), 85–91. Zbl 0398.54001, MR 0493957, 10.1016/0016-660X(78)90020-X
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