A note on the hyperspace of finite subsets

• Autorzy: Tuyen Luong Quoc , Tuyen Ong Van

Identyfikatory

DOI

10.21008/j.0044-4413.2021.0006

• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the relation between a space X satisfying certain generalized metric properties and its hyperspace of finite subsets F(X) satisfying the same properties. We prove that if F(X) is a stric B₀-space then so is X. However, there exists a stric B₀-space X such that Fn(X) is not a stric B₀-space for each n ≥ 2, hence F(X) is not a stric B₀-space. Moreover, we prove that X is a P-space (resp., sequentially separable) if and only if so is F(X).

Słowa kluczowe

EN

symmetric product; hyperspace; sp-network; stric B0-space; P-space; sequentially separable

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2021
• Tom: nr 65
• Strony: 67--73
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Tuyen Luong Quoc

• Department of Mathematics, Da Nang University of Education, 459 Ton Duc Thang Street, Da Nang City, Vietnam

autor

Tuyen Ong Van

• Hoa Vang High School, 101 Ong Ich Duong Street, Da Nang City, Vietnam

Bibliografia

• [1] Arhangel’skii A.V., Tkachenko M.G., Topological Groups and Related Structures, Atlantis Press/World Scientific, Paris-Amsterdam, 2008.
• [2] Davis S.W., More on Cauchy conditions, Topology Proc., 9(1984), 31-36.
• [3] Engelking R., General Topology, Heldermann Verlag, Berlin, 1989.
• [4] Good C., Macías S., Symmetric products of generalized metric spaces, Topology Appl., 206(2016), 93-114.
• [5] Liu X., Liu C., Lin S., Strict Pytkeev networks with sensors and their applications in topological groups, Topology Appl., 258(2019), 58-78.
• [6] Michael E., Bi-quotient maps and cartesian products of quotient maps, Ann. Inst. Fourier, 18(1968), 287-302.
• [7] Peng L.-X., Sun Y., A study on symmetric products of generalized metric spaces, Topology Appl., 231(2017), 411-429.
• [8] Tanaka Y., On quasi-k-spaces, Proc. Japan Acad., 46(1970), 1074-1079.
• [9] Tanaka Y., Tanaka spaces and products of sequential spaces, Comment. Math. Univ. Carolinae, 48(3)(2007), 529-540.
• [10] Tang Z., Lin S., Lin F., Symmetric products and closed finite-to-one mappings, Topology Appl., 234(2018), 26-45.
• [11] Tuyen L.Q., Tuyen O.V., On the n-fold symmetric product of a space with a σ-(P)-property cn-network (ck-network), Comment. Math. Univ. Carolinae, 61(2)(2020), 257-263.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).