中文摘要：

以Beilinson，Bernstein和Deligne（BeilinsonA A，Bernstein J，Deligne P．Faisceaux pervers[J]．AstArique，1982，100：5-171）的工作为基础，应用recollement和紧生成t-结构的定义和性质证明了三角范畴上紧生成的t-结构扩张闭的BBD—induction的形式．利用同余上极限和紧生成的余-t-结构的定义和性质证明了紧生成的余-t-结构的扩张闭也是一个余-t-结构．

英文摘要：

Following the work of Beilinson, Bernstein, and Deligne （Beilinson A A, Bernstein J, Deligne P. Faisceaux pervers [J]. Asterique, 1982, 100： 5-171）, by using the properties of recollement and compactly generated t-structures, we prove the BBD-induction of the extension closure of compactly generated t-structures on triangulated categories. We also show that the extension closure of compactly generated co-t-structures is a co-t-structure with respect to the properties of colimit and compactly generated co-t-structures.