Abstract:
It has introduced the concept of cellular subfunctor in the category COMP of all compact spaces and their mappings. We has proved that the space of all nonempty closed subsets of $X$ is cellular embed to the $\lambda(X\cup \{p\})$. One of the general results proved in this article is the equality $c(F(X))=c(X^{\omega})$ for covariant functors $\mathcal{N}^k, \lambda$ and $G$.
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