Three-space weak barrelledness

Our simple and comprehensive framework consists of the fourteen locally convex space properties that underlie “reinventing weak barrelledness.” Choosing a, b, c from these properties, we determine the truth or falsity of each of the 143 = 2744 statements of the form: If the closed subspace F has property a and E/F has property b, then E necessarily has property c. For all 142 = 196 choices of a, b a necessary condition on c in order that the statement be true is that a ⇒ c and b ⇒ c, and for a majority (100) of these choices the condition is also sufficient. If property a = b = c verifies the statement, it is a three-space property. Exactly seven of the fourteen qualify: the six previously known and Ruess’ property (L). Efficiency in solving (the previously unsolved eight of) these fourteen classic three-space problems is the key to finding all 2744 results, an efficiency defined and fostered by the framework.  2002 Elsevier Science (USA). All rights reserved