FUNCTORIAL PROPERTIES OF THE SPACE Z(X) FOR STRATIFIABLE SPACES
DOI:
https://doi.org/10.46754/jmsi.2023.12.003Abstract
In the realm of stratifiable spaces and their continuous mappings into themselves, a construction ¢ within the domain of Coty, known as the test space, defines a covariant functor within this category. This construction Z defines a functor Z:S→S, which allows each stratifiable space X to be immersed in a closed manner into some other space Z(X), which is a stratifiable space with “good” functorial, geometric and topological properties. It is shown that the functor Z:S'→S' is a normal, open and monadic functor in this category S of stratifiable spaces and continuous mappings into itself. Furthermore, an exploration of the dimensional properties of the space Z(X) is conducted for the stratifiable space X, defined for each n∈N+ subfunctor Zn:S→S of the functor Z, for which the dimension satisfies the inequality: dim Zn(X) ≤ n dim X+n-1.
References
Borges, C. R. (1996). On stratibiable spaces. Pacific Journal of Mathematics, 17(1), 1-16.
Robert, C. (1972). Retractions dans les espaces stratibiables. Bulletin de la Société Mathématique de France, 102, 129-149. https://eudml.org/doc/87222
Borges, C. R. (1969). A study of absolute extensor spaces. Pacific Journal of Mathematics, 31(3), 609-617. https://msp.org/pjm/1969/31-3/pjm-v31-n3-p07-s.pdf
Borsuk, K. (1971). The theory of retracts (pp. 291).Moscow: Mir Publisher.
Robert, C., Bao-Lin, G., & Sakai, K. (1995). The hyperspace of finite subsets of a stratifiable space. Fundamenta Mathematicae, 147, 1-9. https://bibliotekanauki.pl/articles/1208364.pdf
Zhuraev, T. F. (2014). Equivariant analogs of some geometric and topological properties on stratifiable spaces X (pp. 23-27). West. Kirg. Nat. University.
Aleksandrov, P. S., & Pasynkov, B. A. (1973). Introduction to the theory of dimension (pp. 576). Moscow, Izdatel’stvo Nauka.
Zhuraev, T. F. (1989). Some geometric properties of the functor of probabilistic measures and its subfunctors [Doctoral’s Dissertation Thesis, MGU, Moscow].
Banakh, T., Radul, T., & Zarichniy, M. (1996). Absorbing sets in infinite-dimensional manifolds. (Mathematical Studies Monograph Series, Vol. 1). VNTL Publishers.
Zhuraev, T. F. (1992). σ-spaces and functors of finite degree. Reports of Uzbekistan Academy of Sciences, 4-5, 15-18.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Journal of Mathematical Sciences and Informatics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
