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Keywords:
extent; Lindelöf degree; $\Sigma$-space; strict $p$-space; semi-stratifiable
extent; Lindelöf degree; $\Sigma$-space; strict $p$-space; semi-stratifiable
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.
References:
[1] Aull C.E.: A generalization of a theorem of Aquaro. Bull. Austral. Math. Soc. 9 (1973), 105–108. DOI 10.1017/S0004972700042933 | MR 0372817 | Zbl 0255.54015
[2] Burke D.K.: On $p$-spaces and $w\Delta$-spaces. Pacific J. Math. 35 (1970), 285–296. DOI 10.2140/pjm.1970.35.285 | MR 0278255 | Zbl 0204.55703
[3] Creed G.D.: Concerning semi-stratifiable spaces. Pacific J. Math. 32 (1970), 47–54. DOI 10.2140/pjm.1970.32.47 | MR 0254799
[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. MR 0776629 | Zbl 0794.54034
[5] Hajnal A., Juhász I.: Discrete subspaces of topological spaces II. Indag. Math. 31 (1969), 18–30. DOI 10.1016/1385-7258(69)90022-5 | MR 0264585 | Zbl 0169.53901
[6] Hajnal A., Juhász I.: Some remarks on a property of topological cardinal functions. Acta Math. Acad. Sci. Hungar. 20 (1969), 25–37. DOI 10.1007/BF01894566 | MR 0242103 | Zbl 0184.26401
[7] Jiang S.: Every strict p-space is $\theta $-refinable. Topology Proc. 11 (1986), 309–316. MR 0945506 | Zbl 0637.54024
[8] Jones F.B.: Concering normal and completely normal spaces. Bull. Amer. Math. Soc. 43 (1937), 671–677. DOI 10.1090/S0002-9904-1937-06622-5 | MR 1563615
[9] Juhász I.: Cardinal Functions in Topology. Mathematisch Centrum, Amsterdam, 1971. MR 0340021
[10] Juhász I.: Cardinal Functions in Topology – Ten Years Later. Mathematisch Centrum, Amsterdam, 1980. MR 0576927 | Zbl 0479.54001
[11] Kunen K., Roitman J.: Attaining the spread at cardinals of cofinality $\omega $. Pacific J. Math. 70 (1977), 199–205. DOI 10.2140/pjm.1977.70.199 | MR 0462949 | Zbl 0375.54004
[12] Nagami K.: $\varSigma$-spaces. Fund. Math. 65 (1969), 169–192. MR 0257963
[13] Okuyama A.: On a generalization of $\varSigma$-spaces. Pacific J. Math 42 (1972), 485–495. DOI 10.2140/pjm.1972.42.485 | MR 0313995
[14] Roitman J.: The spread of regular spaces. General Topology and Appl. 8 (1978), 85–91. DOI 10.1016/0016-660X(78)90020-X | MR 0493957 | Zbl 0398.54001
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