Abstract
A classC of pointed spaces is called a cellular class if it is closed under weak equivalences, arbitrary wedges and pointed homotopy pushouts. The smallest cellular class containingX is denoted byC(X), and a partial order relation ≪ is defined by:X ≪Y ifY εC(X). In this text we investigate the sub partial order sets generated respectively by simply connected finite CW-complexes and by rational spaces. For rational spaces we prove a unique decomposition theorem, a density theorem and the existence of infinitely many non-comparable elements. We then prove the density theorem for a generic class of finite CW-complexes.
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Felix, Y., Parent, PE. Density and unique decomposition theorems for the lattice of cellular classes. Isr. J. Math. 136, 317–351 (2003). https://doi.org/10.1007/BF02807204
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DOI: https://doi.org/10.1007/BF02807204