A note on set-star-K-Menger spaces
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Sumit Singh
Abstract
A space X is said to have the set-star-K-Menger property if for each nonempty subset A of X and for each sequence (𝓤n : n ∈ ℕ) of collections of open sets in X such that for each n ∈ ℕ, A ⊆ ⋃ 𝓤n, there is a sequence (Kn : n ∈ ℕ) of compact subsets of X such that A ⊆
There exists a T1 set-star-Menger space which is not set-star-K-Menger and there exists a Tychonoff set-star-K-Menger space that is not set-star-Menger.
Assuming 𝔡 = 𝔠, there exists a Tychonoff set-star-K-Menger space having a regular-closed Gδ-subspace which is not set-star-K-Menger.
If the Alexandroff duplicate of a space X is set-star-K-Menger, then X is set-star-K-Menger.
The product of set-star-K-Menger space and a compact space is rectangular set-star-K-Menger space.
The above-mentioned results answer to Problem 2.5 and Problem 3.6, and give a partial answer to Problem 3.11 in [SINGH, S.: On set-star-K-Menger spaces, Publ. Math. Debrecen 100 (2022), 87–100]. Further, we continue to study the topological properties of set-star-K-Menger spaces.
Acknowledgement
The author would like to thank the referees for their valuable remarks and suggestions which greatly improved the paper.
(Communicated by David Buhagiar )
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Articles in the same Issue
- Prof. RNDr. Július korbaš, CSC. passed away
- Kalmbach measurability In d0-algebras
- Quantifiers on L-algebras
- Ideals of functions with compact support in the integer-valued case
- An algebraic study of the logic S5’(BL)
- Triangular numbers and generalized fibonacci polynomial
- A general matrix series inversion pair and associated polynomials
- Quantum ostrowski type inequalities for pre-invex functions
- Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
- Approximating families for lattice outer measures on unsharp quantum logics
- On a generalized Lamé-Navier system in ℝ3
- Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
- On some classical properties of normed spaces via generalized vector valued almost convergence
- Fan-Hemicontinuity for the gradient of the norm in Hilbert space
- Solvability of mixed problems for heat equations with two nonlocal conditions
- The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
- A note on set-star-K-Menger spaces
- A bivariate extension of the Omega distribution for two-dimensional proportional data
- Bernstein polynomials based iterative method for solving fractional integral equations
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