$\lambda$-perfect maps

TL;DR

This paper introduces $5$-perfect maps, a generalization of perfect maps, exploring their properties using $P_5$-spaces and $5$-compactness to extend understanding of map classifications.

Contribution

It presents the concept of $5$-perfect maps and investigates their properties within the framework of $P_5$-spaces and $5$-compactness, expanding the theory of map generalizations.

Findings

$5$-perfect maps generalize perfect maps.

Results relate $5$-perfect maps to $P_5$-spaces.

New properties of $5$-compactness are established.

Abstract

The $\lambda$-perfect maps, a generalization of perfect maps (continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some results regarding $\lambda$-perfect maps will be investigated.