Condensation rank of injective Banach spaces

TL;DR

This paper establishes that the condensation rank of any infinite dimensional injective Banach space is at least the first uncountable ordinal, linking topological properties with Banach space theory.

Contribution

It proves a lower bound for the condensation rank of infinite dimensional injective Banach spaces, a novel connection between topology and functional analysis.

Findings

Condensation rank of infinite dimensional injective Banach spaces is ≥ first uncountable ordinal.

Provides a new topological invariant bound for Banach spaces.

Links topological and geometric properties of Banach spaces.

Abstract

The condensation rank associates any topological space with a unique ordinal number. In this paper we prove that the condensation rank of any infinite dimensional injective Banach space is equal to or greater than the first uncountable ordinal number.