k-almost-quasifibrations

TL;DR

This paper refines the concept of k-almost-quasifibrations to k-c-quasifibrations, exploring their properties and establishing criteria for identifying such maps, thereby advancing the understanding of quasifibration generalizations.

Contribution

It introduces the updated definition of k-c-quasifibrations and generalizes existing quasifibration results to this new class.

Findings

Defines and studies properties of k-c-quasifibribrations.

Provides criteria for recognizing k-c-quasifibrations.

Extends previous quasifibration results to the new framework.

Abstract

In [8](arXiv:2111.06159) 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.