A spectral characterization of skeletal maps

TL;DR

This paper provides a spectral characterization of skeletal maps between realcompact spaces, showing they can be represented as limit maps of skeletal morphisms between w-spectra with surjective projections.

Contribution

It establishes a new spectral criterion for skeletal maps, linking topological properties with spectral morphisms in a novel way.

Findings

Skeletal maps are characterized as limit maps of skeletal morphisms.

The characterization applies to realcompact spaces.

Surjective limit projections are essential in the spectral representation.

Abstract

We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between w-spectra with surjective limit projections.