# Some remarks on the projective properties of Menger and Hurewicz

## TL;DR

This paper explores how the projective versions of Menger and Hurewicz properties in Tychonoff spaces can be characterized through their embeddings in the Čech-Stone compactification, extending known descriptions of these properties.

## Contribution

It provides new characterizations of the projective Menger and Hurewicz properties in terms of their placement within the Čech-Stone compactification.

## Key findings

- Analogous characterizations for projective Menger and Hurewicz properties
- Extension of known space embedding characterizations to projective properties
- Deeper understanding of the relationship between space properties and compactifications

## Abstract

It is known that both the Menger and Hurewicz property of a Tychonoff space $X$ can be described by the way $X$ is placed in its \v{C}ech-Stone compactification $\beta X$. We provide analogous characterizations for the projective versions of the properties of Menger and Hurewicz.