Subspaces of sequential spaces
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 407-413
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