Abstract
1. Introduction. All spaces in this paper are Hausdorff. We recall that a space X is sequentially compact, if every countable subset of X contains a convergent sequence. Let us consider the three statements:(1) Every compact space of cardinality ≤ ʗ contains a point of countable character.(2) Every compact space of cardinality ≤ ʗ is sequentially compact.(3) Every infinite compact space of cardinality ≤ ʗ contains a convergent sequence.
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