Abstract

The set theoretic principle ♢ is used to construct hereditarily Lindelof, non-separable subspaces of given complete spaces of countable tightness. The construction is patterned after R. B. Jensen's original use of ♢ to construct a Souslin line, and yields the following result: Suppose X is a regular space of countable tightness having weight at most c. If no non-empty G δ set in X is contained in a separable subspace of X, and if either X is countably complete or has all closed subsets Baire, then X contains an L-space.

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