Geodesic
On the family of sequentially proper topologies on the space of maps
Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 102-108.

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This contribution investigates the properties of the space $C(X,Y)$ of continuous maps with the greatest sequentially proper topology. The main results of the research are necessary and sufficient conditions for admissibility and properness in the terms of Arens–Dugundji obtained for this topology. 
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D. S. Frolova. On the family of sequentially proper topologies on the space of maps. Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 102-108. http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a12/

[1] Arens R., “A topology for spaces of transformations”, Annals of Math., 47 (1946), 480–495 | DOI | MR | Zbl

[2] Arens R., Dugundji J., “Topologies for function spaces”, Pacific J. Math., 1 (1951), 5–31 | DOI | MR | Zbl

[3] Georgiu D. N., Iliadis S. D., Papadopulos B. K., “Topologii prostranstv funktsii”, Zapiski nauchnykh seminarov POMI, 208, 1993, 82–97

[4] Escardo M., Lawson J., Simpson A., “Comparing cartesian closed categories of (core) compactly generated spaces”, Top. Appl., 143 (2004), 105–145 | DOI | MR | Zbl

[5] Timokhovich V. L., Frolova D. S., “O maksimalnoi sekventsialno sobstvennoi topologii na mnozhestve otobrazhenii”, Vestnik BGU. Ser. 1, 2012, no. 3, 102–107 | MR

[6] Engelking R., Obschaya topologiya, M., 1986

[7] Hart K. P., Nagata J., Vaughan J. E., Encyclopedia of General Topology, Elsevier, 2004 | MR

[8] Wiscamb M. R., “The discrete countable chain condition”, Proc. Amer. Math. Soc., 23 (1969), 608–612 | DOI | MR | Zbl

[9] Mcintyre D. W., “Compact-calibres of regular and monotonically normal spaces”, Int. J. Math. Math. Sci., 29:4 (2002), 209–216 | DOI | MR | Zbl

[10] Kukrak G. O., Timokhovich V. L., “O predele obratnogo spektra eksponentsialnykh prostranstv”, Vestnik BGU. Ser. 1, 2001, no. 1, 51–55

[11] Timokhovich V. L., Frolova D. S., “O sobstvennosti i dopustimosti v smysle Arensa–Dugundzhi infimuma topologii ravnomernoi skhodimosti”, Dokl. NAN Belarusi, 56:2 (2012), 22–26 | MR | Zbl

[12] Blair R. L., “Chain conditions in para-lindelof and related spaces”, Top. Proc., 11 (1986), 247–266 | MR | Zbl

[13] Navy C., Paralindelöf versus paracompact, Thesis, University of Wisconsin, 1981

[14] Goldovt I. Yu., Timokhovich V. L., “Nasyscheniya topologicheskikh prostranstv i problema Morita”, Dokl. AN BSSR, 21:9 (1977), 777–780 | MR | Zbl

[15] Levin M. A., Timokhovich V. L., “M-prostranstva i schetnokompaktifitsiruemost”, Dokl. AN BSSR, 23:3 (1979), 213–216 | MR | Zbl

[16] Fox R. H., “On topologies for function spaces”, Bull. Amer. Math. Soc., 51 (1945), 429–432 | DOI | MR | Zbl