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Keywords:
preimage; open map; complete metric space; $F$-space; $F$-lattice; compact set; uniformly open map; surpositive operator; lower semicontinuous set-valued map
Summary:
We discuss various results on the existence of `true' preimages under continuous open maps between $F$-spaces, $F$-lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.
References:
[1] Aliprantis C., Burkinshaw O.: Locally Solid Riesz Spaces with Applications to Economics. Mathematical Surveys and Monographs, 105, American Mathematical Society, Providence, 2003. DOI 10.1090/surv/105 | MR 2011364
[2] Bessaga C., Pełczyński A.: Selected Topics in Infinite-Dimensional Topology. Monografie Matematyczne, 58, PWN---Polish Scientific Publishers, Warsaw, 1975. MR 0478168
[3] Bourbaki N.: Éléments de mathématique. I: Les structures fondamentales de l'analyse. Fascicule VIII. Livre III: Topologie générale. Chapitre 9: Utilisation des nombres réels en topologie générale. Deuxième édition revue et augmentée, Actualités Scientifiques et Industrielles, 1045, Hermann, Paris, 1958 (French). MR 0173226
[4] Diestel J.: Sequences and Series in Banach Spaces. Graduate Texts in Mathematics, 92, Springer, New York, 1984. MR 0737004
[5] Drewnowski L., Wnuk W.: On finitely generated vector sublattices. Studia Math. 245 (2019), no. 2, 129–167. DOI 10.4064/sm170524-23-12 | MR 3863066
[6] Engelking R.: General Topology. Biblioteka Matematyczna, Tom 47, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). MR 0500779 | Zbl 0684.54001
[7] Jarchow H.: Locally Convex Spaces. Mathematische Leitfäden, B. G. Teubner, Stuttgart, 1981. MR 0632257 | Zbl 0466.46001
[8] Köthe G.: Topological Vector Spaces. I. Die Grundlehren der mathematischen Wissenschaften, 159, Springer, New York, 1969. MR 0248498
[9] Michael E.: A theorem on semi-continuous set-valued functions. Duke Math. J. 26 (1959), 647–651. DOI 10.1215/S0012-7094-59-02662-6 | MR 0109343
[10] Michael E.: $\aleph_0$-spaces. J. Math. Mech. 15 (1966), 983–1002. MR 0206907
[11] Michael E.: $G_\delta$ sections and compact-covering maps. Duke Math. J. 36 (1969), 125–127. DOI 10.1215/S0012-7094-69-03617-5 | MR 0240790
[12] Michael E., K. Nagami: Compact-covering images of metric spaces. Proc. Amer. Math. Soc. 37 (1973), 260–266. DOI 10.1090/S0002-9939-1973-0307148-4 | MR 0307148
[13] Nagami K.: Ranges which enable open maps to be compact-covering. General Topology and Appl. 3 (1973), 355–367. DOI 10.1016/0016-660X(73)90023-8 | MR 0345055
[14] Schaefer H. H.: Banach Lattices and Positive Operators. Die Grundlehren der mathematischen Wissenschaften, 215, Springer, New York, 1974. MR 0423039 | Zbl 0296.47023
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