My recent work on the border of topology and metric/distance geometry, by Maria Moszynska

Topology Atlas Document # zaab-12.htm | Production Editor: R. Flagg

Topology Atlas Invited Contributions, vol. 1, issue 4 (1996), 52.

My recent work on the border of topology and metric/distance geometry
by

Maria Moszynska

(University of Warsaw, Poland)

Recently I have published four papers (one joint) on metric counterparts of basic topological constructions, as products, inverse limits, and direct limits. Their list is the following:

1. On metric products (with I.Herburt), Coll.Math. 62(1991), 121-133.

2. On metric inverse limits, Journal London Math. Soc. (2)42 (1990), 160-174.

3. On the uniqueness problem for metric products, Glasnik Mat. 27(47) (1992), 145-158.

4. Lipschitz inverse and direct sequences, Topology Appl. 56 (1994), 259-275.

The paper [1] concerns various classes of metric spaces and multiplicativity of these classes with respect to product (with different product metrics).

The uniqueness problem for metric products is a generalization of the following famous Ulam problem #77(b) in the Scottish Book: Is it true that if squares of two metric spaces are isometric, then the spaces themselves are isometric? The paper [3] contains a partial solution.

The papers [2] and [4] concern metric inverse and direct limits (in fact in [2] only the notion of metric inverse limit was introduced, the other was defined in [4]). In [4], using topological methods I presented a simple proof of a result concerning contunuity of the Hausdorff measure for some class of submanifolds of Euclidean n-space. (The result was due to Federer, but its original proof was terribly complicated).

Metric inverse limits were applied to fractal geometry by Krzysztof Rudnik in his paper "Self-similar metric inverse limits of invariant geometric inverse sequences", Topology Appl. 48 (1992), 1-17 (doctoral dissertation).

Received by the editors: January 9, 1996.