countability axioms

countability axioms

[‚kau̇n·tə′bil·əd·ē ‚ax·sē·əmz]
(mathematics)
Two conditions which are satisfied by a euclidean space and one or the other of which is often assumed in the study of a general topological space; the first states that any point in the topological space has a countable local base, while the second states that the topological space has a countable base.
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The first seven chapters cover the usual topics of point-set or general topology, including topological spaces, new spaces from old ones, connectedness, the separation and countability axioms, and metrizability and paracompactness, as well as special topics such as contraction mapping in metric spaces, normed linear spaces, the Frechet derivative, manifolds, fractals, compactifications, the Alexander subbase, and the Tychonoff theorems.