Convergence in van der Waerden and Hindman spaces

DOI10.1016/J.TOPOL.2014.10.019zbMATH Open1307.54007OpenAlexW2001766434MaRDI QIDQ471493

Rafał Filipów, Jacek Tryba

Publication date: 14 November 2014

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

Full work available at URL: https://doi.org/10.1016/j.topol.2014.10.019

zbMATH Keywords

van der Waerden theoremHindman theoremcountably compact spacesequentially compact space\(\mathcal{I}\)-convergenceHindman spaceP-idealvan der Waerden space

Mathematics Subject Classification ID

Topological characterizations of particular spaces (54F65) Topological spaces and generalizations (closure spaces, etc.) (54A05) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Consistency and independence results in general topology (54A35)

Cites Work

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• On Hindman spaces and the Bolzano-Weierstrass property
• Topics in topology
• \(\ell\)-selection principles for sequences of functions
• The Scarborough-Stone problem for Hausdorff spaces
• Analytic ideals and their applications
• Van der Waerden spaces
• Hindman spaces
• Statistical Limit Points
• Semiselective coideals
• Analytic quotients: theory of liftings for quotients over analytic ideals on the integers
• Van der Waerden spaces and Hindman spaces are not the same
• A brief remark on van der Waerden spaces
• Ideal convergence of bounded sequences
• The reaping and splitting numbers of nice ideals
• A new kind of compactness for topological spaces
• On completely regular spaces

Related Items (10)

A brief remark on van der Waerden spaces ⋮ Convergence of functions and their Moreau envelopes on Hadamard spaces ⋮ On Hindman spaces and the Bolzano-Weierstrass property ⋮ The ideal test for the divergence of a series ⋮ Unboring ideals ⋮ Vahlen theorem for two-dimensional convergents ⋮ Homogeneous ideals on countable sets ⋮ Ultrafilters and the Katětov order ⋮ Spaces not distinguishing ideal convergences of real-valued functions. II ⋮ New Hindman spaces

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