8 papers · 1 filter
Functional countability and exponential separability of product spaces and subspaces
Rodrigo Hernández-Gutiérrez, Rodrigo Hernández-Gutiérrez, Santi Spadaro
We investigate the behavior of functional countability and exponential separability in products and subspaces of topological spaces. We solve a problem of Tkachuk by showing that t…
On (non-Menger) spaces whose closed nowhere dense subsets are Menger
Mathieu Baillif, Santi Spadaro
A space is od-Menger if it satisfies , where are the collection of covers of by respectively open subsets and op…
Comparing functional countability and exponential separability
Rodrigo Hernández-Gutiérrez, Santi Spadaro
A space is functionally countable if every real-valued continuous function has countable image. A stronger property recently defined by Tkachuk is exponentially separability. We st…
On some recent selective properties involving networks
Maddalena Bonanzinga, Davide Giacopello, Santi Spadaro +1
In this paper we investigate R-,H-, and M-{\it nw}-selective properties introduced in \cite{BG}. In particular, we provide consistent uncountable examples of such spaces and we def…
Consistency and independence phenomena involving cellular-Lindelof spaces
Rodrigo Hernández-Gutiérrez, Santi Spadaro
The cellular-Lindelöf property is a common generalization of the Lindelöf property and the countable chain condition that was introduced by Bella and Spadaro in 2018. We solve tw…
Strongly discrete subsets with Lindelöf closures
Angelo Bella, Santi Spadaro
We define a topological space to be an "SDL space" if the closure of each one of its strongly discrete subsets is Lindelöf. After distinguishing this property from the Lindelöf p…