On some recent selective properties involving networks
-
Maddalena Bonanzinga
,
Santi Spadaro
Abstract
In this paper, we investigate R-, H-, and M-nw-selective properties introduced in [Bonanzinga, M.—Giacopello, D.: A generalization of M-separability by networks, Atti Accad. Peloritana dei Pericolanti Cl. Sci. Fis. Mat. Nat. 101(2) (2023), A11]. In particular, we provide consistent uncountable examples of such spaces and we define trivial R-, H-, and M-nw-selective spaces the ones with countable net weight having, additionally, the cardinality and the weight strictly less then cov(𝓜), 𝔟, and 𝔡, respectively. Since we establish that spaces having cardinalities more than cov(𝓜), 𝔟, and 𝔡, fail to have the R-, H-, and M-nw-selective properties, respectively, non-trivial examples should eventually have weight greater than or equal to these small cardinals. Using forcing methods, we construct consistent countable non-trivial examples of R-nw-selective and H-nw-selective spaces and we establish some limitations to constructions of non-trivial examples. Moreover, we consistently prove the existence of two H-nw-selective spaces whose product fails to be M-nw-selective. Finally, we study some relations between nw-selective properties and a strong version of the HFD property.
(Communicated by L'ubica Holá)
Acknowledgement
The first two authors in alphabetical order would like to thank the “National Group for Algebric and Geometric Structures, and their Applications”(GNSAGA-INdAM) for their invaluable support throughout the course of this research. The research of the fourth author was funded in whole by the Austrian Science Fund (FWF) [DOI 10.55776/I5930 and 10.55776/PAT5730424]. A part of the research was completed while the fourth author was visiting the third one at the University of Palermo in Fall 2023, the fourth author would like to thank the third one for his great hospitality.
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Artikel in diesem Heft
- A note on the coprime power graph of groups
- Simplified axiomatic system of DRl-semigroups
- Special filters in bounded lattices
- Reichenbach’s causal completeness of quantum probability spaces
- A construction of magmas and related representation
- Extensions of the triangular D(3)-Pair {3, 6}
- Hermite-Hadamard type inequalities for new class h-convex mappings utilizing weighted generalized fractional integrals
- Divergence operator of regular mappings
- Monotonicity of the ratio of two arbitrary gaussian hypergeometric functions
- Oscillation and asymptotic criteria for certain third-order neutral differential equations involving distributed deviating arguments
- Multiplicity results for a fourth-order elliptic equation of p(x)-kirchhoff type with weights
- Singular discrete dirac equations
- Convergence of bivariate exponential sampling series in logarithmic weighted spaces of functions
- Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application
- Existence of solutions and Hyers-Ulam stability for κ-fractional iterative differential equations
- On almost cosymplectic generalized (k, μ)ʹ-spaces
- On some recent selective properties involving networks
- Minimal usco and minimal cusco maps and the topology of pointwise convergence
- Corrigendum to: Every positive integer is a sum of at most n + 2 centered n-gonal numbers
