A note on the Arens' space and sequential fan

DOI10.1016/S0166-8641(97)00031-XzbMath0885.54019MaRDI QIDQ1375158

Lin, Shou

Publication date: 22 April 1998

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

\(k\)-network\(k\)-spacesequential fanArens' space

Mathematics Subject Classification ID

Sequential spaces (54D55) Topological spaces with richer structures (54E99) Topological characterizations of particular spaces (54F65) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20)

Related Items (37)

\(S_{2}\) and the Fréchet property of free topological groups ⋮ Submetrizability and first-countability of coset spaces ⋮ Sequential rectifiable spaces of countable \(\mathrm {cs}^*\)-character ⋮ Selection principles in function spaces with the compact-open topology ⋮ \textit{snf}-countability and \textit{csf}-countability in \(F_{4}(X)\) ⋮ \(so\)-metrizable spaces and images of metric spaces ⋮ \(\mathfrak{P}_0\)-spaces ⋮ \(S_\omega\) and \(S_2\) on free topological groups ⋮ Symmetric products and closed finite-to-one mappings ⋮ Sequential properties of function spaces with the compact-open topology ⋮ Topological classification of function spaces with the Fell topology. III. ⋮ \(\mathcal{I}_{sn}\)-sequential spaces and the images of metric spaces ⋮ Weak countability axioms of coset spaces ⋮ On paratopological groups ⋮ \textit{cs}-Regular families, \textit{cs}-finite families and the images of metric spaces ⋮ The first-countability of paratopological left-loops ⋮ Point-countable covers and sequence-covering \(s\)-mappings at subsets ⋮ Fréchet-Urysohn fans in free topological groups ⋮ Networks on free topological groups ⋮ Strict Pytkeev networks with sensors and their applications in topological groups ⋮ The \(k_{R}\)-property of free abelian topological groups and products of sequential fans ⋮ Sequence-covering maps of metric spaces ⋮ Metrizable and weakly metrizable coset spaces ⋮ \(k^*\)-metrizable spaces and their applications ⋮ On products of \(k\)-spaces ⋮ Generalized metric spaces with algebraic structures ⋮ On weak bases ⋮ Some questions on partial metric spaces ⋮ On the Weak-Open Images of Metric Spaces ⋮ A Note on $$\aleph$$ -Spaces and g-Metrizable Spaces ⋮ Point-regular covers and sequence-covering compact mappings ⋮ Remainders in compactifications of topological groups ⋮ Products of symmetric spaces, and \(k\)-networks ⋮ The closed finite-to-one mappings and their applications ⋮ Countable tightness and \(k\)-property of free topological vector spaces ⋮ Mappings on weak Cauchy \(sn\)-symmetric spaces ⋮ On the countable tightness of product spaces

Cites Work

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• Characterizations of \(\aleph\)-spaces
• Spaces which contain a copy of \(S_{\omega}\) or \(S_ 2\) and their applications
• Metrizability of topological groups having weak topologies with respect to good covers
• Point-countable \(k\)-networks, closed maps, and related results
• \(g\)-metrizability and \(S_ \omega\)
• On defining a space by a weak base
• Sequential order of product spaces
• Spaces determined by point-countable covers
• Ordinal invariants for topological spaces
• Metrizabillity of certain quotient space
• Products of Sequential Spaces
• Spaces in which sequences suffice II
• MAPPINGS AND SPACES
• A quintuple quotient quest
• Note on Convergence in Topology

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