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On (Strongly) (Θ-)Discrete Homogeneous Spaces

  • Vitalij A. Chatyrko and Alexandre Karassev EMAIL logo
Published/Copyright: December 18, 2023
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 73 Issue 6

ABSTRACT

We introduce the classes of (strongly) Θ-discrete homogeneous spaces. We discuss the relationships of these classes to other classes of spaces possessing homogeneity-related properties, such as (strongly) n-homogeneous spaces. Many examples are given distinguishing discrete homogeneity and other types of homogeneity.

2020 Mathematics Subject Classification: Primary 57S05; Secondary 54F99; 54A10
Keywords: (strong) discrete homogeneity; (strong) n-homogeneity; Bing space; Ritter space

(Communicated by L’ubica Holá)

Funding statement: The second author was partially supported by NSERC Grant 257231-15.

4. Appendix

The Bing space B ([Bi]) is the rational half plane { (x,y)∈ℚ×ℚ:y≥0 } endowed with the topology τ consisting of the sets U⊂B such that for every point (a, b) ∈ U there exists ϵ > 0 such that

{ (x,0)∈B:| x−(a−b/3) |<ϵ }∪{ (x,0)∈B:| x−(a+b/3) |<ϵ }⊂U.

Note that Cl U1∩Cl U2∩Cl U3=0 , where U1 ={(x, 0) ∈ B: 0 < x < 1}, U2 = {(x, 0) ∈ B : 2 < x < 3} and U3 = {(x, 0) ∈ B: 4 < x < 5}.

Acknowledgement

The authors are grateful to the anonymous referee for remarks and suggestions that improved the manuscript.

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Received: 2022-08-15
Accepted: 2023-02-25
Published Online: 2023-12-18

© 2023 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2023-0115
Keywords for this article
(strong) discrete homogeneity; (strong) n-homogeneity; Bing space; Ritter space

Articles in the same Issue

  1. ℒ-fuzzy Annihilators in Residuated Lattices
  2. Regular Double p-Algebras: A Converse to a Katriňák Theorem and Applications
  3. Uniform Local Connectedness and Completion of Metric σ-Frames
  4. On Transcendental Regular Continued Fractions
  5. On Repdigits Which are Sums or Differences of Two k-Pell Numbers
  6. Peirce Decompositions for Evolution Algebras
  7. Generalized Anti-Symmetry Laws in Groupoids
  8. New Bounds of Cyclic Jensen’s Differences via Weighted Hadamard Inequalities with Applications
  9. Geometric Properties of Generalized Bessel Function Associated with the Exponential Function
  10. On the Attainable Set of Iterative Differential Inclusions
  11. On the Differential-Difference Sine-Gordon Equation with an Integral Type Source
  12. A Critical p(x)-Laplacian Steklov Type Problem with Weights
  13. Distributivity of a Uni-nullnorm with Continuous and Archimedean Underlying T-norms and T-conorms Over an Arbitrary Uninorm
  14. Some Approximation Properties of Operators Including Degenerate Appell Polynomials
  15. Operators that are Weakly Coercive and a Compact Perturbation
  16. On the Structure Lie Operator of a Real Hypersurface in the Complex Quadric
  17. Paracompactness and Open Relations
  18. On (Strongly) (Θ-)Discrete Homogeneous Spaces
  19. The Alpha Power Muth-G Distributions and Its Applications in Survival and Reliability Analyses
  20. Weakly Einstein Equivalence in a Golden Space Form and Certain CR-submanifolds
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