2016/10/14 by István Juhász, Juhász, I., Vladimir V. Tkachuk +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #54A25 #54D20 #54F05 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Mathematical and Theoretical Analysis #Rings, Modules, and Algebras #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1610.04506
openalex publication_date 2016/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We call a space X it weakly linearly Lindel "of if for any family\n\U of non-empty open subsets of X of regular uncountable\ncardinality \κ, there exists a point x\∈ X such that every\nneighborhood of x meets \κ-many elements of \U. We also\nintroduce the concept of it almost discretely Lindel "of spaces as the ones\nin which every discrete subspace can be covered by a Lindel "of subspace. We\nprove that, in addition to linearly Lindel "of spaces, both weakly Lindel "of\nspaces and almost discretely Lindel "of spaces are weakly linearly Lindel "of.\n The main result of the paper is formulated in the title. It implies, among\nother things, that every weakly Lindel "of monotonically normal space is\nLindel "of; this result seems to be new even for linearly ordered topological\nspaces.\n We show that, under the hypothesis 2^\ω < \ω_\ω, if the\nco-diagonal \ΔcX=(X\× X)\∖ \ΔX of a space X is\ndiscretely Lindel "of, then X is Lindel "of and has a weaker second countable\ntopology; here \ΔX= (x,x): x\∈ X is the diagonal of the space X.\nMoreover, the discrete Lindel "ofness of \ΔcX together with the\nLindel "of \Σ-property of X imply that X has a countable network.\n