Z/p-acyclic resolutions in the strongly countable Z/p-dimensional case

Details Z/p-acyclic resolutions in the strongly countable Z/p-dimensional case Z/p-acyclic resolutions in the strongly countable Z/p-dimensional case

2011-01-13

arxiv.org/abs/1101.2480v1

Mathematics

Geometric Topology

16 pages, submitted to Topology Proceedings

Scientific paper

We prove the following Theorem: Let X be a nonempty compact metrizable space, let $l_1 \leq l_2 \leq...$ be a sequence of natural numbers, and let $X_1 \subset X_2 \subset...$ be a sequence of nonempty closed subspaces of X such that for each k in N, $dim_{Z/p} X_k \leq l_k < \infty$. Then there exists a compact metrizable space Z, having closed subspaces $Z_1 \subset Z_2 \subset...$, and a surjective cell-like map $\pi: Z \to X$, such that for each k in N, (a) $dim Z_k \leq l_k$, (b) $\pi (Z_k) = X_k$, and (c) $\pi | {Z_k}: Z_k \to X_k$ is a Z/p-acyclic map. Moreover, there is a sequence $A_1 \subset A_2 \subset...$ of closed subspaces of Z, such that for each k, $dim A_k \leq l_k$, $\pi|{A_k}: A_k\to X$ is surjective, and for k in N, $Z_k\subset A_k$ and $\pi|{A_k}: A_k\to X$ is a UV^{l_k-1}-map. It is not required that X be the union of all X_k, nor that Z be the union of all Z_k. This result generalizes the Z/p-resolution theorem of A. Dranishnikov, and runs parallel to a similar theorem of S. Ageev, R. Jim\'enez, and L. Rubin, who studied the situation where the group was Z.

Affiliated with

Also associated with

No associations

Rating

Z/p-acyclic resolutions in the strongly countable Z/p-dimensional case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Z/p-acyclic resolutions in the strongly countable Z/p-dimensional case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Z/p-acyclic resolutions in the strongly countable Z/p-dimensional case will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-65773