Iterations of Resolvents and Homogeneous Cut-Point Spaces
Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 288-299.

Voir la notice de l'article provenant de la source Math-Net.Ru

An approach describing the spaces of iterations of resolvents with constant mappings is given. Its use allows one to construct (homogeneous, not algebraically homogeneous) cut-point spaces of arbitrary order.
Keywords: resolvent, iteration of a resolvent, cut-point space, compact Hausdorff space, base for a topology, homeomorphism of spaces, connected space, fiber.
@article{MZM_2015_98_2_a12,
     author = {M. S. Shulikina},
     title = {Iterations of {Resolvents} and {Homogeneous} {Cut-Point} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {288--299},
     publisher = {mathdoc},
     volume = {98},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a12/}
}
TY  - JOUR
AU  - M. S. Shulikina
TI  - Iterations of Resolvents and Homogeneous Cut-Point Spaces
JO  - Matematičeskie zametki
PY  - 2015
SP  - 288
EP  - 299
VL  - 98
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a12/
LA  - ru
ID  - MZM_2015_98_2_a12
ER  - 
%0 Journal Article
%A M. S. Shulikina
%T Iterations of Resolvents and Homogeneous Cut-Point Spaces
%J Matematičeskie zametki
%D 2015
%P 288-299
%V 98
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a12/
%G ru
%F MZM_2015_98_2_a12
M. S. Shulikina. Iterations of Resolvents and Homogeneous Cut-Point Spaces. Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 288-299. http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a12/

[1] V. V. Fedorchuk, “O bikompaktakh s nesovpadayuschimi razmernostyami”, Dokl. AN SSSR, 182:2 (1968), 275–277 | Zbl

[2] V. V. Fedorchuk, “Vpolne zamknutye otobrazheniya i ikh prilozheniya”, Fundament. i prikl. matem., 9:4 (2003), 105–235 | MR | Zbl

[3] S. Watson, “The construction of topological spaces. Planks and resolutions”, Recent Progress in General Topology, North-Holland, Amsterdam, 1992, 673–757 | MR | Zbl

[4] A. M. Sokolovskaya, “Odin metod postroeniya polureshetok bikompaktnykh $G$-rasshirenii”, Matem. zametki, 82:6 (2007), 916–925 | DOI | MR | Zbl

[5] D. Daniel, W. S. Mahavier, “Concerning cut point spaces of order three”, Int. J. Math. Math. Sci., 2007, Art. ID 10679 | MR | Zbl

[6] L. R. Ford, Jr., “Homeomorphism groups and coset spaces”, Trans. Amer. Math. Soc., 77 (1954), 490–497 | DOI | MR | Zbl

[7] R. Engelking, Obschaya topologiya, Mir, M., 1986 | MR | Zbl

[8] K. Kuratovskii, Topologiya, T. 2, Mir, M., 1969 | MR

[9] C. Bessaga, A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, Monografie Matematyczne, 58, PWN, Warszawa, 1975 | MR | Zbl

[10] B. Honari, Y. Bahrampour, “Cut-point spaces”, Proc. Amer. Math. Soc., 127:9 (1999), 2797–2803 | DOI | MR | Zbl

[11] K. L. Kozlov, V. A. Chatyrko, “Topologicheskie gruppy preobrazovanii i bikompakty Dugundzhi”, Matem. sb., 201:1 (2010), 103–128 | DOI | MR | Zbl