On structural numbers of topological spaces
-
Vitalij A. Chatyrko
Abstract
Zero-dimensional structural numbers
for any metrizable space X with dim X = n ≥ 0, we have
for any countable-dimensional metrizable space Y, we have
Funding statement: The second author was partially supported by NSERC Discovery Development Grant.
Acknowledgement
The authors thank the anonymous referees for valuable suggestions that helped to improve the paper.
-
(Communicated by David Buhagiar)
References
[AN] Aarts, J. M.—Nishiura, T.: Dimension and Extensions, North-Holland, Amsterdam, 1993.Search in Google Scholar
[B] Bing, R. H.: Metrization of topological spaces, Canad. J. Math. 3 (1951), 175–186.10.4153/CJM-1951-022-3Search in Google Scholar
[Bi] Birkhoff, G.: On combination of topologies, Fund. Math. 26 (1936), 156–166.10.4064/fm-26-1-156-166Search in Google Scholar
[ChH] Chatyrko, V. A.—Hattori, Y.: A poset of topologies on the set of real numbers, Comment. Math. Univ. Carolin. 54(2) (2013), 189–196.Search in Google Scholar
[D] Van Douwen, E. K.: The small inductive dimension can be raised by the adjunction of a single point, Indag. Math. 53 (1973), 434–442.10.1016/1385-7258(73)90067-XSearch in Google Scholar
[E1] Engelking, R.: General Topology, Heldermann Verlag, Berlin, 1989.Search in Google Scholar
[E2] Engelking, R.: Theory of Dimensions. Finite and Infinite, Heldermann Verlag, Lemgo, 1995.Search in Google Scholar
[GHMS] Georgiou, D.—Hattori, Y.—Megaritis, A.—Sereti, F.: Zero-dimensional extensions of topologies, Topology Appl. (2025), Art. ID 109252.10.1016/j.topol.2025.109252Search in Google Scholar
[H] Hanner, O.: Solid spaces and absolute retracts, Ark. för Mat. 1 (1951), 375–382.10.1007/BF02591374Search in Google Scholar
[LA] Larson, R. E.—Andima, S. J.: The lattice of topologies: a survey, Rocky Mountain J. Math. 5 (1975), 177–198.10.1216/RMJ-1975-5-2-177Search in Google Scholar
[MW] Mcintyre, D. W.—Watson, W. S.: Finite intervals in the partial orders of zero-dimensional, Tychonoff and regular topologies, Topology Appl. 139(1–3) (2004), 23–36.10.1016/j.topol.2003.08.010Search in Google Scholar
[M] Morita, K.: On the dimension of the product of topological spaces, Tsukuba J. Math. 1 (1977), 1–6.10.21099/tkbjm/1496158375Search in Google Scholar
[P] Przymusinski, T. C.: A note on dimension theory of metric spaces, Fund. Math. 85 (1974), 277–284.10.4064/fm-85-3-277-284Search in Google Scholar
[R] Roy, P.: Failure of equivalence of dimension concepts for metric spaces, Bull. Amer. Math. Soc. 68 (1962), 609–613.10.1090/S0002-9904-1962-10872-6Search in Google Scholar
[SW] Steprans, J.—Watson, S.: Mutually complementary families of T1 topologies, equivalence relations and partial orders, Proc. Amer. Math. Soc. 123(7) (1995), 2237–2249.10.1090/S0002-9939-1995-1301530-9Search in Google Scholar
© 2025 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
- Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
- Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
