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selections; l.s.c. set-valued maps; mesocompact; sequentially mesocompact; persevering compact set-valued maps

References:

[1] Boone J.R.: **Some characterization of paracompactness in $\chi $-space**. Fund. Math. 72 (1971), 145–155. MR 0295291

[2] Choban M.: **Many-valued mappings and Borel sets, II**. Trans. Moscow Math. Soc. 23 (1970), 286–310.

[3] Engelking R.: **General Topology**. Revised and completed edition, Heldermann, Berlin, 1989. MR 1039321 | Zbl 0684.54001

[4] Michael E.: **A theorem on semicontinuous set-valued funtions**. Duke Math. 26 (1956), 647–652. DOI 10.1215/S0012-7094-59-02662-6 | MR 0109343

[5] Michael E.: **Topologies on spaces of subsets**. Trans. Amer. Math. Soc. 71 (1951), 152–182. DOI 10.1090/S0002-9947-1951-0042109-4 | MR 0042109 | Zbl 0043.37902

[6] Miyazaki K.: **Characterizations of paracompact-like properties by means of set-valued semi-continuous selections**. Proc. Amer. Math. Soc. 129 (2001), 2777–2782. DOI 10.1090/S0002-9939-01-06204-9 | MR 1838802 | Zbl 0973.54009

[7] Nedev S.: **Selection and factorization theorems for set-valued mapings**. Serdica 6 (1980), 291–317. MR 0644284

[8] Yan P.-F.: **$\tau$ selections and its applictions on BCO**. J. Math. (in Chinese) 17 (1997), 547–551. MR 1675535