On $\alpha$-embedded sets and extension of mappings

TL;DR

This paper introduces the concept of lpha-embedded sets and uses them to extend the Kuratowski Extension Theorem, broadening the understanding of set embeddings and mapping extensions in topology.

Contribution

The paper defines lpha-embedded sets and generalizes the Kuratowski Extension Theorem using these sets, providing new tools for topological mapping extensions.

Findings

lpha-embedded sets are effectively characterized.

The generalized Kuratowski Extension Theorem applies to a wider class of sets.

New methods for extending mappings in topology are developed.

Abstract

We introduce and study $\alpha$-embedded sets and apply them to generalize the Kuratowski Extension Theorem.