The Menger and projective Menger properties of function spaces with the set-open topology
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Alexander V. Osipov
Abstract
For a Tychonoff space X and a family λ of subsets of X, we denote by Cλ(X) the space of all real-valued continuous functions on X with the set-open topology.
A Menger space is a topological space in which for every sequence of open covers 𝓤1, 𝓤2, … of the space there are finite sets 𝓕1 ⊂ 𝓤1, 𝓕2 ⊂ 𝓤2, … such that family 𝓕1 ∪ 𝓕2 ∪ … covers the space.
In this paper, we study the Menger and projective Menger properties of a Hausdorff space Cλ(X). Our main results state that
Cλ(X) is Menger if and only if Cλ(X) is σ-compact;
Cp(Y | X) is projective Menger if and only if Cp(Y | X) is σ-pseudocompact where Y is a dense subset of X.
(Communicated by David Buhagiar)
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© 2019 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
- Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
Articles in the same Issue
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
- Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
