Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778037 | Topology and its Applications | 2017 | 26 Pages |
Abstract
We study the combinatorial size of subsets of a ballean, as defined in [19,23] (largeness, smallness, extralargeness, etc.), paying particular attention to the preservation of these properties under taking images and inverse images along various classes of maps (bornologous, effectively proper, (weakly) soft, coarse embeddings, canonical projections of products, canonical inclusions of co-products, etc.). We show by appropriate examples that many of the properties describing the size are not preserved under coarse equivalences (even injective or surjective ones), whereas largeness and smallness are preserved under arbitrary coarse equivalences.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Dikran Dikranjan, Nicolò Zava,