Abstract
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.
Similar content being viewed by others
References
V. V. Fedorchuk, “Bicompacta with noncoinciding dimensionalities,” Dokl. Akad. Nauk SSSR 182 (2), 275–277 (1968) [SovietMath. Dokl. 9 (2), 1148–1150 (1968)].
V. V. Fedorchuk, “Fully closed mappings and their applications,” Fundam. Prikl. Mat. 9 (4), 105–235 (2003) [J. Math. Sci. (New York) 136 (5), 4201–4292 (2006)].
S. Watson, “The construction of topological spaces: Planks and resolutions,” in Recent Progress in General Topology (North-Holland, Amsterdam, 1992), pp. 673–757.
A. M. Sokolovskaya, “A method for constructing semilattices of G-surjections,” Mat. Zametki 82 (6), 916–925 (2007) [Math. Notes 82 (5–6), 827–835 (2007)].
D. Daniel and W. S. Mahavier, “Concerning cut point spaces of order three,” Int. J. Math. Math. Sci., No. Art. ID 10679 (2007).
L. R. Ford, Jr., “Homeomorphism groups and coset spaces,” Trans. Amer. Math. Soc. 77, 490–497 (1954).
R. Engelking, General Topology (PWN, Warsaw, 1977; Mir, Moscow, 1986).
K. Kuratowski, Topology (Academic Press, New York–London, 1966; Mir, Moscow, 1966), Vol. 2.
C. Bessaga and A. Pelczyński, Selected Topics in Infinite-Dimensional Topology, inMonografieMatematyczne (PWN, Warszawa, 1975), Vol. 58.
B. Honari and Y. Bahrampour, “Cut-point spaces,” Proc. Amer. Math. Soc. 127 (9), 2797–2803 (1999).
K. L. Kozlov and V. A. Chatyrko, “Topological transformation groups and Dugundji compacta,” Sb. Math. 201, No. 1, 103–128 (2010 Mat. Sb. 201 (1), 103–128 (2010) [Sb. Math. 201 (1–2), 103–128 (2010)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M. S. Shulikina, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 2, pp. 288–299.
Rights and permissions
About this article
Cite this article
Shulikina, M.S. Iterations of resolvents and homogeneous cut-point spaces. Math Notes 98, 316–324 (2015). https://doi.org/10.1134/S0001434615070330
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434615070330