In this paper, we investigate how a (topological) statement about accumulation points of subsets of T1 topological spaces relates to various weak choice principles. Most of the principles under discussion are weak versions (more precisely, restrictions) of the principle of dependent choices (DC). For instance, our topological statement (which turns out to be equivalent to the statement “All infinite sets are Dedekind-infinite”) implies the restriction of DC to lattices in which all principal ideals are finite. We also discuss in which ways several weak choice principles are related to each other, posing a number of questions. 

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Q_A_30_2012_1_8_topological_statement.pdf