Subspaces of sequential spaces
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 407-413
Cet article a éte moissonné depuis la source Math-Net.Ru
It is proved that the space of continuous functions on the ordinary closed interval with the topology of pointwise convergence is not subsequential. In sequential spaces satisfying certain conditions, subspaces dense-in-themselves without convergent sequences are found; such subspaces are constructed in certain sequential compact spaces and semitopological groups.
@article{MZM_1998_64_3_a8,
author = {V. I. Malykhin},
title = {Subspaces of sequential spaces},
journal = {Matemati\v{c}eskie zametki},
pages = {407--413},
year = {1998},
volume = {64},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a8/}
}
V. I. Malykhin. Subspaces of sequential spaces. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 407-413. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a8/
[1] Pytkeev E. G., “O maksimalnoi razlozhimosti prostranstv”, Tr. MIAN, 154, Nauka, M., 1983, 209–213 | MR | Zbl
[2] Malykhin V. I., Tironi G., “Weakly FU-spaces”, Quaderni Matematica. II Serie, no. 386, Univ. di Trieste, 1996, 1–9
[3] Arkhangelskii A. V., Topologicheskie prostranstva funktsii, Izd-vo MGU, M., 1989
[4] Bella A., Malykhin V. I., “Around tight point”, Topology Appl., 20 (1997), 1–8 | DOI | MR
[5] Uspenskii V. V., “O spektre chastot funktsionalnykh prostranstv”, Vestn. MGU. Ser. 1. Matem., mekh., 1982, no. 1, 31–35 | MR | Zbl
[6] Nedev S., Choban M. M., “O metrizuemosti topologicheskikh grupp”, Vestn. MGU. Ser. 1. Matem., mekh., 1968, no. 6, 18–20 | MR | Zbl