是闭集 英语是什么意思 - 英语翻译

• is closed

在 中文 中使用 是闭集 的示例及其翻译为 英语

是闭集，当且仅当它含有所有它的极限点。
Is closed if and only if it contains all of its limit points.

一个线性泛函是连续的，当且仅当其核是闭集。
A linear functional is continuous if and only if its kernel is closed.

在X中是闭集。
Is closed in X.

特别的，空集和全空间是闭集。
In particular, the empty set and the whole space are closed.

集合S是闭集，当且仅当S=cl(S)。
A set S is closed if and only if S= ci(S).

等价地，一个集合是闭集当且仅当所有的极限点都是这个集合中的点。
Equivalently, a set is closed if and only if it contains all of its limit points.

在Rn内，一个集合是紧集当且仅当它是闭集并且有界。
In Rn, a set is compact if and only if it is closed and bounded.

在Rn内，一个集合是紧集当且仅当它是闭集并且有界。
In a Euclidean space, a set is compact if and only if it is closed and bounded.

希尔伯特-施密特算子的集合在范数拓扑下是闭集，当且仅当H是有限维空间。
The set of Hilbert- Schmidt operators is closed in the norm topology if, and only if, H is finite-dimensional.

在Rn内，一个集合是紧集当且仅当它是闭集并且有界。
Theorem A subset of Rn is compact if and only if it is closed and bounded.

如果f是连续函数并且Y是豪斯多夫空间则ker(f)是闭集。
If f is continuous and Y is Hausdorff then ker(f) is closed.

一般的说，等价类[x]会是闭集，当且仅当这个空间是对称的。
In general, the equivalence classes[x] will be closed if and only if the space is symmetric.

是闭集，当且仅当它含有所有它的极限点。
A set is closed if and only if it contains all its limit points.

若A是闭集，则A包含S当且仅当A包含cl(S)。
If A is a closed set, then A contains S if and only if A contains cl(S).

下部集合↓x总是闭集；但是上部集合↑x不必须是开集或闭集。
The lower set↓x is always closed; however, the upper set↑x need not be open or closed.

由于V(r)的补集是闭集，且含有U(r)，因此从最后一个条件可以推出上面的条件(2)。
Since the complement of V(r) is closed and contains U(r), the latter condition then implies condition(2) from above.

欧几里得空间Rn的子集是紧致的，当且仅当它是闭集并且是有界的。
A subset of Euclidean space Rn is compact if and only if it is closed and bounded.

如果A是一个开集或闭集，且是Rn(甚至Borel集，见度量空间，待补)的子集，那么A是勒贝格可测的。
If A is an open or closed subset of Rn(or even Borel set, see metric space), then A is Lebesgue measurable.

唯一的闭集是空集和X。
The only closed sets are the empty set and X.

尽管是在非常空洞意义上，因为仅有的闭集是∅和X。
All in a rather vacuous way though, since the only closed sets are∅ and X.

但是上部集合↑x不必须是开集或闭集。
However, the upper set↑x need not be open or closed.

等价地说，A在X中稠密当且仅当X中唯一包含A的闭集是X自己。
Equivalently, A is dense in X if and only if the only closed subset of X containing A is X itself.

用較花巧的术语来说，不相交闭集不只是由鄰域分离的，还是由函数分离的。
(In fancier terms, disjoint closed sets are not only separated by neighbourhoods, but also separated by a function.).

Cl(S)是包含S的最小的闭集。
Ci(S) is the smallest closed set containing S.

另外，如果一个非空的完备度量空间是可数个闭集的并集，那么其中一个闭集具有非空的内部。
Also: if a non-empty complete metric space is the countable union of closed sets, then one of these closed sets has non-empty interior.

等价的说，X是完美正规的，当且仅当所有闭集是零集合。
Equivalently, X is perfectly normal if and only if every closed set is a zero set..

如果f是连续函数并且Y是豪斯多夫空间则ker(f)闭集。
If f is continuous and Y is Hausdorff then ker(f) is closed.

明显的X是完美正规的，当且仅当X是正规的并且所有闭集是Gδ集合。
It turns out that X is perfectly normal if and only if X is normal and every closed set is a Gδ set..