k-almost-quasifibrations

In 8 we introduced the notion of a k-almost-quasifibration. In this article we update this definition and call it a k-c-quasifibration. This will help us to relate it to quasifibrations. We study some basic properties of k-c-quasifibrations. We also generalize a series of results on quasifibrations ([1]) to k-c-quasifibrations giving criteria for a map to be a k-c-quasifibration.