Lindelöf P-spaces need not be Sokolov
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Vladimir V. Tkachuk
Abstract
We show that for every Lindelöf P-space a weaker version of the Sokolov property holds. Besides, if K is a scattered Eberlein compact space and X is obtained from K by declaring open all Gδ-subsets of K, then X is monotonically Sokolov. The proof of this statement uses the fact that every Lindelöf subspace of a scattered Eberlein compact space must be σ-compact; this result seems to be interesting in itself. We also give an example of a Lindelöf P-space X such that Cp(X) has uncountable extent. In particular, neither X nor Cp(X) has the Sokolov property.
Research supported by CONACyT grant CB-2012-01-178103 (Mexico).
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- State hoops
- On derivations of partially ordered sets
- Interior and closure operators on commutative basic algebras
- When is the cayley graph of a semigroup isomorphic to the cayley graph of a group
- Sequences of cantor type and their expressibility
- δ-Fibonacci and δ-lucas numbers, δ-fibonacci and δ-lucas polynomials
- Law of inertia for the factorization of cubic polynomials – the case of primes 2 and 3
- Closed hereditary coreflective subcategories in epireflective subcategories of Top
- Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments
- Difference of two strong Światkowski lower semicontinuous functions
- Fejér-type inequalities (II)
- Representation of maxitive measures: An overview
- On a conjecture of Y. H. Cao and X. B. Zhang
- On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces
- Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups
- Homological properties of banach modules over abstract segal algebras
- Variable Hajłasz-Sobolev spaces on compact metric spaces
- Commuting pairs of self-adjoint elements in C*-algebras
- Additivity of maps preserving products AP ± PA* on C*-algebras
- A note on derived connections from semi-symmetric metric connections
- Lindelöf P-spaces need not be Sokolov
- Strong convergence properties for arrays of rowwise negatively orthant dependent random variables
- Least absolute deviations problem for the Michaelis-Menten function
- Congruence pairs of principal p-algebras
