Topology Proceedings 33 (2009), pp. 107-121

Ideals and sequentially compact spaces

Jana Flašková

We say that a topological space X is an I_[1/n]-space if for every sequence 〈x_n 〉_{n ∈ N} in X there exists a converging subsequence 〈x_{n_k} 〉_{k ∈ N} with ∑_{k ∈ w}[1/(n_k)] = ∞. Every \Sm-space is sequentially compact, but not every sequentially compact space is I_[1/n]-space.

Assuming Martin's axiom for s-centered posets we construct a van der Waerden space that is not an I_[1/n]-space and an I_[1/n]-space that is not Hindman.

Keywords: sequentially compact space, van der Waerden space, Hindman space, F_s-ideal

Mathematics Subject Classification: 54G99 03E50 (54H05 05C55)

Document formats: PDF file 196.7 Kb

Topology Proceedings, Volume 33 (2009)
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