Abstract
It is shown that from any first-countable, zero-dimensional, locally compact, non-DFCC space X with the property that every nonempty open set has π-weight c one can construct a pseudocompact space Y + that is not strongly 2-star-Lindelöf. Such a space Y + would therefore be 1. (1) 2-starcompact, T 3 but not strongly 2-starcompact; 2. (2) 2-star-Lindelöf, T 3 but not strongly 2-star-Lindelöf. A space satisfying (1) has been constructed using CH and a Moore space with a σ-locally countable base satisfying (2) is known. The examples generated here are easier than these two spaces, require no set theory beyond ZFC and make the distinctions (1) and (2) simultaneously.
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