Kakol, Jerzy; Moll López, Santiago Emmanuel(Springer-Verlag, 2021-07)
[EN] It is well known that the property of being a bounded set in the class of topological vector spaces E is not a topological property, where a subset B ¿ E is called a bounded set if every neighbourhood of zero U in E ...
For a Banach space E and its bidual space E'', the function k(H) defined on bounded
subsets H of E measures how far H is from being σ(E,E')-relatively compact in E. This concept, introduced independently by Granero, ...
Kakol, Jerzy; López Pellicer, Manuel(Cambridge University Press, 2012)
The paper deals with the following problem: characterize Tichonov spaces X whose realcompactification ¿X is a Lindelöf ¿-space. There are many situations (both in topology and functional analysis) where Lindelöf ¿ (even ...
Ferrer, Jesús; Kakol, Jerzy; López Pellicer, Manuel; Wójtowicz, Marek(Adam Mickiewicz University The Faculty of Mathematics and Computer Science, 2011)
[EN] Corson's example shows that there exists a Banach space EE which is not weakly normal but EE contains a closed subspace isomorphic to the Banach space C[0,1]C[0,1] and such that the quotient space E/C[0,1]E/C[0,1] is ...
[EN] A subset Y of the dual closed unit ball B_{E*} of a Banach space E is called a Rainwater set for E if every bounded sequence of E that converges pointwise on Y converges weakly in E. In this paper, topological properties ...
[EN] While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of infinite-dimensional separable quotients in some Banach spaces of vector-valued ...
[EN] Following Schachermayer, a subset B of an algebra A of subsets of Ω is said to have the N-property if a B-pointwise bounded subset Mof ba(A)is uniformly bounded on A, where ba(A) is the Banach space of the real ...
Using the index of Nagami we get new topological cardinal inequalities for spaces Cp(X).
A particular case of Theorem 1 states that if L ⊆ Cp(X) is a Lindelöf Σ-space and the
Nagami index Nag(X) of X is less or equal ...