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Weak barrelledness for C(X) spaces by Jerzy Ka̧kol; Stephen A. Saxon; Aaron R. Todd is a Mathematics article available to read on EtoBox.

What is Weak barrelledness for C(X) spaces about?

Buchwalter and Schmets reconciled C c (X) and C p (X) spaces with most of the weak barrelledness conditions of 1973, but could not determine if א 0 -barrelled ⇔ ∞ -barrelled for C c (X). The areas grew apart. Full reconciliation with the fourteen conditions adopted by Saxon and Sánchez Ruiz needs their 1997 characterization of Ruess' property (L), which allows us to reduce the C c (X) problem to its 1973 status and solve it by carefully translating the topology of Kunen (1980) andvan Mill (1982) to find the example that eluded Buchwalter and Schmets. The more tractable C p (X) readily partitions the conditions into just two equivalence classes, the same as for metrizable locally convex spaces, instead of the five required for C c (X) spaces. Our paper elicits others, soon to appear, that analytically characterize when the Tychonov space X is pseudocompact, or Warner bounded, or when C c (X) is a df -space (Jarchow's 1981 question).

Who reads Weak barrelledness for C(X) spaces?

Author

Jerzy Ka̧kol; Stephen A. Saxon; Aaron R. Todd

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)

Published

2004

Language

EN

Field

Mathematics (Physical Sciences)