科研之友
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摘要
A space X is said to be weakly quasi-first-countable if and only if for all x is an element of X, there exists countably many countable families of decreasing subsets containing x such that a set O is open if and only if for any x is an element of O, O contains a member of each family associated to x. For a space X, we denote the countable a-product of X endowed with the box topology by sigma B(X). We prove that if X is first-countable and locally compact, then sigma B(X) is weakly quasi-first-countable, which gives a general method to construct weakly quasi-first-countable spaces which are neither weakly first-countable nor quasi-first-countable.
