On rectangular inverse systems of topological spaces

For every cofinite inverse system of compact Hausdorff spaces X = (X, p\u27, ), there exists a cofinite inverse system of compact polyhedra Z = (Z, r\u27\u27, × T) and there are mappings u : X Z, (, ) × T, such that u p\u27 = r\u27\u27 u\u27, for \u27. Moreover, for every , the mapping u : X Z = (Z, r\u27\u27, T), given by the mappings u\u27, T, is a limit of Z. If mappings p : X X form a limit p : X X, then the mappings v = u p : X Z form a limit v : X Z. An analogous result holds for cofinite inverse systems of topological spaces and ANR-resolutions (polyhedral resolutions)

Some forms of Eastern Mediterranean relief ware from the Archaeological Museum in Split

U radu se objavljuju primjerci reljefnih korintskih zdjelica i knidske antropomorfne keramike koji se čuvaju u Arheološkome muzeju u Splitu. Obje vrste keramike izvozile su se na prostor zapadnog Mediterana premda ne u velikim količinama.Examples of Corinthian small relief bowls and Cnidian anthropomorphic ware held in the Archaeological Museum are published. Both types of ware were imported to the Western Mediterranean, albeit not in large quantities

Thirty years of shape theory

The paper outlines the development of shape theory since its founding by K. Borsuk 30 years ago to the present days. As a motivation for introducing shape theory, some shortcomings of homotopy theory in dealing with spaces of irregular local behavior are described. Special attention is given to the contributions to shape theory made by the Zagreb topology group

Elementary examples of essential phantom mappings

It is known that essential phantom mappings (of the second kind) between connected CW-complexes do exist. However, it appears that in the literature there are few explicit examples of such mappings. One usually finds descriptions of the domain and the codomain and an existence proof that the set of homotopy classes of mappings from the domain to the codomain is infinite. The purpose of the present paper is to describe some elementary examples of essential phantom mappings. The codomain is the n-sphere S^n, n ≥ 2, and the domain is the telescope Tn, associated with the sequence of copies of the canonical mapping f : S^n-1 → S^n-1 of odd degree p > 1. There are no essential phantom mappings whose codomain is the 1-sphere S^1

Extension dimension of inverse limits

Recently L.R. Rubin and P.J. Schapiro have considered inverse sequences X of metrizable spaces Xi, whose extension dimension dim Xi ≤ P, i.e., P ∈ AE(Xi), where P is an arbitrary polyhedron (or CW-complex). They proved that dim X ≤ P, where X = lim X. The present paper generalizes their result to inverse sequences of stratifiable spaces, giving at the same time a more conceptual proof

Extension dimension of inverse limits. Correction of a proof

The erroneous proof of a lemma in a previous paper of the author on extension dimension of inverse limits is replaced by a correct one