Contents

# Contents

## Definition

###### Definition

A cell spectrum is a topological sequential spectrum $X$ realized as the colimit over a sequence of spectra $\ast = X_0 \to X_1 \to X_2 \to X_3 \to \cdots$ such that there are morphisms

$j_n \;\colon\; \left( \underset{i \in I_n}{\sqcup} \Sigma^\infty S^{q_n} \right) \longrightarrow X_n$

with $X_{n+1}= Cone(j_n)$ (the mapping cone).

A cell spectrum is a CW-spectrum if each attaching map $\Sigma^\infty S^{q_n}\to X_n$ factors through a $X_k \to X_n$ with $k \lt q$.

###### Definition

A CW-spectrum, def. , is called a finite spectrum (or countable spectrum, etc.) if it has finitely many cells (countably many cells) according to def. .

## References

Discussion in the generality of equivariant spectra is in

• L. Gaunce Lewis, Peter May, and M. Steinberger (with contributions by J.E. McClure), section I.5 of Equivariant stable homotopy theory Springer Lecture Notes in Mathematics Vol.1213. 1986 (pdf)

Last revised on May 18, 2016 at 05:07:39. See the history of this page for a list of all contributions to it.