Spaces of continuous characteristic functions
We show that if is first-countable, of countable extent, and a subspace of some ordinal, then is Lindelöf.
Spaces of continuous step functions over LOTS
We investigate spaces over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of over LOTS. We also characterize countably compact LOTS whose is linearly Lindelöf for each n. Both the necessary conditions and the characterization are given in terms of the topology of the Dedekind completion of a LOTS.
Spaces whose connected expansion preserve connected subsets
Spaces with Boolean assemblies
Splittability for ordered topological spaces
In quest'articolo dimostriamo come il concetto «spezzabilità», formulato e sviluppato di Arhangel'skii, viene trasferito dallo studio di spazi topologici a quello di spazi topologici parzialmente ordinati. Otteniamo numerosi risultati in forma «se è spezzabile (facendo uso di funzioni appropriatamente scelte) su spazi che hanno una proprietà, allora anche soddisfa la stessa proprietà».
Stationary sets and paracompactness in ordered spaces: a survey
Stationary sets, trees and continuums.
Stone lattices: a topological approach
Subparacompactness in Cartesian products of generalized ordered topological spaces