On ωI-covers
Abstract
This work focuses on presenting what we have called ωI-covers, where I is a non-principal ideal on some topological space X. These covers are a generalization of what is known in the literature as ω-covers and it turns out that the ωI-covers satisfy many properties analogous to these, in particular, we show that an X space satisfies an specific selection principle in terms of the ωI-covers if and only if it satisfies a Ramsey type relation, which generalizes a classic result for the ω-covers that was proved in Scheepers (1996) and in Just et al. (1996).
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