# K-stability of continuous C(X)-algebras

## TL;DR

This paper investigates the K-stability of continuous C(X)-algebras with K-stable fibers, proving that under certain topological conditions on X, the entire algebra inherits K-stability.

## Contribution

It establishes that continuous C(X)-algebras with K-stable fibers are K-stable when the base space is compact, metrizable, and finite-dimensional.

## Key findings

- K-stability of fibers implies K-stability of the algebra under specified conditions
- The result applies to compact, metrizable, finite-dimensional spaces
- Provides criteria for inheriting K-stability in continuous C(X)-algebras

## Abstract

A C*-algebra is said to be K-stable if its nonstable K-groups are naturally isomorphic to the usual K-theory groups. We study continuous $C(X)$-algebras, each of whose fibers are K-stable. We show that such an algebra is itself K-stable under the assumption that the underlying space $X$ is compact, metrizable, and of finite covering dimension.