On Weak Uniformity
by
S. A. Peregudov

Part 1. Some results concerning spaces with countably weakly uniform bases are generalized for spaces with n-in-countable ones. A few results concern n-in-finite bases. All spaces are assumed to be T₁. The main results are:

Theorem 1. Let n be a natural number. A regular countably compact space with an n-in-countable T₁ - separating open cover is metrizable.

Theorem 2. Let n be a natural number. A regular locally separable space with an n-in-countable base is metrizable.

Part 2. Two Boolean algebras of many-valued mappings are examined. Automorphisms relative to which a free set is an invariant are defined. A number of notions prove to be in duality. In particular, the weak uniformity is dual to the almost disjointness. Some results are applied to topology.

Date received: June 17, 1999