# Article

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Keywords:
extent; Lindelöf degree; $G_\delta$-diagonal; point-countable base
Summary:
In [The sup = max problem for the extent of generalized metric spaces, Comment. Math. Univ. Carolin. The special issue devoted to Čech 54 (2013), no. 2, 245–257], the author and Yajima discussed the sup = max problem for the extent and the Lindelöf degree of generalized metric spaces: (strict) $p$-spaces, (strong) $\Sigma$-spaces and semi-stratifiable spaces. In this paper, the sup = max problem for the Lindelöf degree of spaces having $G_\delta$-diagonals and for the extent of spaces having point-countable bases is considered.
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] Creed G.D.: Concerning semi-stratifiable spaces. Pacific J. Math. 32 (1970), 47–54. DOI 10.2140/pjm.1970.32.47 | MR 0254799
[3] 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
[4] 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
[5] 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
[6] Hirata Y., Yajima Y.: The sup = max problem for the extent of generalized metric spaces. Comment. Math. Univ. Carolin. (The special issue devoted to Čech) 54 (2013), no. 2, 245–257. MR 3067707 | Zbl 1289.54024
[7] Hodel R.E.: Cardinal functions I. Handbook of Set-theoretic Topology (K. Kunen and J.E. Vaughan, eds), North-Holland, Amsterdam, 1984, pp. 1–61. MR 0776620 | Zbl 0559.54003
[8] Kunen K.: Luzin spaces. Topology Proc. 1 (1976), 191–199. MR 0450063 | Zbl 0389.54004
[9] Kunen K.: Set Theory. An Introduction to Independence Proofs. North-Holland, Amsterdam, 1980. MR 0597342 | Zbl 0534.03026
[10] Roitman J.: The spread of regular spaces. Gen. Topology Appl. 8 (1978), 85–91. DOI 10.1016/0016-660X(78)90020-X | MR 0493957 | Zbl 0398.54001
[11] Yajima Y.: private communication.

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