中文摘要：

首先引入层双保序算子空间中（ωα,υα）-F紧集的概念,并给出它的若干刻画。其次,说明它弱于（ωα,υα）-紧集,但也是Lowen意义下好的推广。再次,讨论（ωα,υα）-F紧性的一些拓扑不变性质。最后,建立（ωα,υα）-F紧性和（ωα,υα）--分离性之间的关系。

英文摘要：

In this paper,firstly,the concept of（ωα,υα）-Fcompact set is introduced in（ωα,υα）-biopos.Its characteristic properties are deplored accordingly.Furthermore,（ωα,υα）-F compactness is weak than（ωα,υα）-compactness,yet it is also a good extension in the sense of Lowen＇s meaning,which preserves many topological invariant properties.Finally,the relations between（ωα,υα）-F compactness and（ωα,υα）-separation axioms are established.