sequentially compact造句

;Sequentially compact : A space is sequentially compact if every sequence has a convergent subsequence.
;Sequentially compact : A space is sequentially compact if every sequence has a convergent subsequence.
The topological space [ 0, ? 1 ) is sequentially compact but not second countable.
Every sequentially compact space is countably compact, and every first-countable, countably compact space is sequentially compact.
Every sequentially compact space is countably compact, and every first-countable, countably compact space is sequentially compact.
It's difficult to find sequentially compact in a sentence. 用sequentially compact造句挺难的

It is almost trivial to prove that the product of two sequentially compact spaces is sequentially compact one passes to a subsequence for the first component and then a subsubsequence for the second component.
If a space is a metric space, then it is sequentially compact if and only if it is product of 2 ^ { \ aleph _ 0 } = \ mathfrak c copies of the closed unit interval ).
The space of all real numbers with the standard topology is not sequentially compact; the sequence " n " ) } } for all natural numbers " n " is a sequence that has no convergent subsequence.
An only slightly more elaborate continuum many copies of the closed unit interval ( with its usual topology ) fails to be sequentially compact with respect to the product topology, even though it is compact by Tychonoff's theorem ( e . g ., see ).