Metrizability vs. Fréchet-Uryshon property
Copyright policy )Metrizability vs. Fréchet-Uryshon property
In metrizable spaces, points in the closure of a subsetAAare limits of sequences inAA; i.e., metrizable spaces are Fréchet-Uryshon spaces. The aim of this paper is to prove that metrizability and the Fréchet-Uryshon property are actually equivalent for a large class of locally convex spaces that includes(LF)(LF)- and(DF)(DF)-spaces. We introduce and study countable bounded tightness of a topological space, a property which implies countable tightness and is strictly weaker than the Fréchet-Urysohn property. We provide applications of our results to, for instance, the space of distributionsD′(Ω)\mathfrak {D}’(\Omega ). The spaceD′(Ω)\mathfrak {D}’(\Omega )is not Fréchet-Urysohn, has countable tightness, but its bounded tightness is uncountable. The results properly extend previous work in this direction.
- University of Florida United States
- Adam Mickiewicz University in Poznań Poland
- University of Murcia Spain
countable bounded tightness, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), locally convex space, Spaces defined by inductive or projective limits (LB, LF, etc.), countable tightness, Function spaces in general topology, General theory of locally convex spaces, Barrelled spaces, bornological spaces, topology of pointwise convergence, Locally convex Fréchet spaces and (DF)-spaces, Uniform structures and generalizations, Metric spaces, metrizability, Cardinality properties (cardinal functions and inequalities, discrete subsets), metrizability, Fréchet-Urysohn property, Compactness in topological linear spaces; angelic spaces, etc.
countable bounded tightness, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), locally convex space, Spaces defined by inductive or projective limits (LB, LF, etc.), countable tightness, Function spaces in general topology, General theory of locally convex spaces, Barrelled spaces, bornological spaces, topology of pointwise convergence, Locally convex Fréchet spaces and (DF)-spaces, Uniform structures and generalizations, Metric spaces, metrizability, Cardinality properties (cardinal functions and inequalities, discrete subsets), metrizability, Fréchet-Urysohn property, Compactness in topological linear spaces; angelic spaces, etc.
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).31 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!