
TL;DR
This paper investigates the concept of $A$-complexity in topological spaces, demonstrating that when $A$ is a sphere localized at a set of primes, the $A$-complexity of any space is at most 1, indicating low complexity.
Contribution
The paper establishes that the $A$-complexity of spaces is at most 1 when $A$ is a sphere localized at a set of primes, advancing understanding of $A$-cellular spaces.
Findings
$A$-complexity of spaces is at most 1 for sphere localizations.
Introduces the concept of $A$-complexity as a measure of building difficulty.
Provides bounds on the complexity of $A$-cellular spaces.
Abstract
An -cellular space is a space built from and its suspensions, analogously to the way that -complexes are built from and its suspensions. The -cellular approximation of a space is an -cellular space which is closest to among all -cellular spaces. The -complexity of a space is an ordinal number that quantifies how difficult it is to build an -cellular approximation of . In this paper, we study spaces with low complexity. In particular we show that if is a sphere localized at a set of primes then the -complexity of each space is at most 1.
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