# On quasi $\kappa$-metrizable spaces

## TL;DR

This paper explores quasi κ-metrizable spaces, a class that remains stable under arbitrary products and extends Shchepin's κ-metrizable spaces, providing new insights into their structure and properties.

## Contribution

It introduces and studies the class of quasi κ-metrizable spaces, expanding the understanding of metrizable space subclasses and their invariance properties.

## Key findings

- Quasi κ-metrizable spaces are invariant under arbitrary products.
- This class properly contains Shchepin's κ-metrizable spaces.
- The paper characterizes the relationship between quasi κ-metrizable and κ-metrizable spaces.

## Abstract

The aim of this paper is to investigate the class of quasi $\kappa$-metrizable spaces. This class is invariant with respect to arbitrary products and contains Shchepin's $\kappa$-metrizable spaces as a proper subclass.