例句與造句

1. For instance, an example of a first-countable space which is not second-countable is counterexample # 3, the discrete topology on an uncountable set.
2. If " X " is a first-countable space and countable choice holds, then the converse also holds : any function preserving sequential limits is continuous.
3. I know that a space X is Lindel鰂 if every open cover has a countable subcover and that X is a second countable space of its topology has a countable basis.
4. I also know that the a second countable space is Lindel鰂 but in order for a Lindel鰂 space to be second countable, our space in question must be a metric space.
5. :A non-empty Hausdorff topological space is a continuous image of the unit interval if and only if it is a compact, connected, locally connected second-countable space.
6. It's difficult to find countable space in a sentence. 用countable space造句挺難的
7. Thus, if one has a countable base for a topology then one has a countable local base at every point, and hence every second countable space is also a first-countable space.
8. Thus, if one has a countable base for a topology then one has a countable local base at every point, and hence every second countable space is also a first-countable space.
9. *PM : sequentially continous implies continuous in a first-countable space, id = 8700 new !-- WP guess : sequentially continous implies continuous in a first-countable space-- Status:
10. *PM : sequentially continous implies continuous in a first-countable space, id = 8700 new !-- WP guess : sequentially continous implies continuous in a first-countable space-- Status:
11. Lindel鰂's lemma is also known as the statement that every open cover in a second-countable space has a countable subcover ( Kelley 1955 : 49 ) This means that every second-countable space is also a Lindel鰂 space.
12. Lindel鰂's lemma is also known as the statement that every open cover in a second-countable space has a countable subcover ( Kelley 1955 : 49 ) This means that every second-countable space is also a Lindel鰂 space.
13. For non first-countable spaces, sequential continuity might be strictly weaker than continuity . ( The spaces for which the two properties are equivalent are called sequential spaces . ) This motivates the consideration of nets instead of sequences in general topological spaces.
14. A well-ordered set as topological space is a first-countable space if and only if it has order type less than or equal to ? 1 ( omega-one ), that is, if and only if the set is countable or has the smallest uncountable order type.
15. Although spaces satisfying such properties had implicitly been studied for several years, the first formal definition is originally due to S . P . Franklin in 1965, who was investigating the question of " what are the classes of topological spaces that can be specified completely by the knowledge of their convergent sequences ? " Franklin arrived at the definition above by noting that every first-countable space can be specified completely by the knowledge of its convergent sequences, and then he abstracted properties of first countable spaces that allowed this to be true.
16. Although spaces satisfying such properties had implicitly been studied for several years, the first formal definition is originally due to S . P . Franklin in 1965, who was investigating the question of " what are the classes of topological spaces that can be specified completely by the knowledge of their convergent sequences ? " Franklin arrived at the definition above by noting that every first-countable space can be specified completely by the knowledge of its convergent sequences, and then he abstracted properties of first countable spaces that allowed this to be true.
更多例句：  上一頁(yè)