函数空间C_k(X)上的T-Tightness和Set-Tightness

T-Tightness and Set-Tightness in Function Space C_k(X)

讨论了函数空间Ck(X)在赋予紧开拓扑下的T-tightness和set-tightness性质,利用开k覆盖获得了Ck(X)是T-tightness空间和set-tightness空间的两个对偶定理,将点态收敛拓扑函数空间Cp(X)的相关结论推广到紧开拓扑函数空间Ck(X)上.

This paper discussed the T-tightness and set-tightness properties in function space Ck （X） with compact-open topology obtained two dualities of Ck （X） being T-tightness space and set-tightness space by means of opening k-cover and generalized the related results from point-wise convergence topology space Cp （X） to compact open topology space Ck （X）.