Corrections to “Oxtoby's Pseudocompleteness Revisited”: [Topology and its Applications 100 (2000) 119–132]

Melvin Henriksen, Harvey Mudd College


The first assertion in Theorem 3.10 is incorrect. (Suppose X is the unit interval [0, 1], let Bn = {[a, b]: a, b ∈ X, a < b}, for n ∈ ω, and let A = (0, 1]. Although A is present for the Oxtoby sequence (Bn), the induced sequence (Bn|A) of π0-bases fails to be an Oxtoby sequence for A since ((0, 1/2n))n is an associated nest with empty intersection.) This impacts the remainder of the paper as follows: (1) Theorem 3.10 relates to an open question of Aarts and Lutzer [1]: Is every dense Gδ-subspace of a pseudocomplete space pseudocomplete? As is noted in [2, 3.9J], this inheritance is well-known for Baire in place of pseudocomplete. The following replacement for Theorem 3.10 improves the inheritance of Baire at the cost of a stronger property for the superspace; it also performs, as will be seen, some of the duties assigned to the original.