“topological space”的概念、定义、习题解题方法及翻译-数学辞典

单词

topological space

释义

topological space

A set X with an associated set T of subsets of X that includes the empty set and the whole set X, and which is closed under arbitrary union and finite intersection. The members of T are the open sets of X, and T is known as the topology. A metric space is a topological space, but not all topologies are metrizable (i.e. arise from a metric), for example, the topology consisting of just the empty set and X. See continuous function, separation axioms.

A sequence xn in a topological space X has limit l if every neighbourhood of l contains a tail of the sequence xn. In a general topological space, sequential convergence does not determine the topology. A set A may have a limit point x which is not the limit of any sequence in A. See net.

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