منابع مشابه
Cohomological Dimension Theory of Compact Metric Spaces
0. Introduction 1 1. General properties of the cohomological dimension 2 2. Bockstein theory 6 3. Cohomological dimension of Cartesian product 10 4. Dimension type algebra 15 5. Realization theorem 19 6. Test spaces 24 7. Infinite-dimensional compacta of finite cohomological dimension 28 8. Resolution theorems 33 9. Resolutions preserving cohomological dimensions 41 10. Imbedding and approximat...
متن کاملEmbedding Finite Metric Spaces in Low Dimension
This paper presents novel techniques that allow the solution to several open problems regarding embedding of finite metric spaces into Lp. We focus on proving near optimal bounds on the dimension with which arbitrary metric spaces embed into Lp. The dimension of the embedding is of very high importance in particular in applications and much effort has been invested in analyzing it. However, no ...
متن کاملEffective dimension in some general metric spaces
We introduce the concept of effective dimension for a general metric space. Effective dimension was defined by Lutz in (Lutz 2003) for Cantor space and has also been extended to Euclidean space. Our extension to other metric spaces is based on a supergale characterization of Hausdorff dimension. We present here the concept of constructive dimension and its characterization in terms of Kolmogoro...
متن کاملOn Dimension Partitions in Discrete Metric Spaces
Let (W,d) be a metric space and S = {s1 . . . sk} an ordered list of subsets of W . The distance between p ∈ W and si ∈ S is d(p, si) = min{ d(p, q) : q ∈ si }. S is a resolving set forW if d(x, si) = d(y, si) for all si implies x = y. A metric basis is a resolving set of minimal cardinality, named the metric dimension of (W,d). The metric dimension has been extensively studied in the literatur...
متن کاملConditional Dimension in Metric Spaces: A Natural Metric-Space Counterpart of Kolmogorov-Complexity-Based Mutual Dimension
It is known that dimension of a set in a metric space can be characterized in information-related terms – in particular, in terms of Kolmogorov complexity of different points from this set. The notion of Kolmogorov complexity K(x) – the shortest length of a program that generates a sequence x – can be naturally generalized to conditional Kolmogorov complexity K(x : y) – the shortest length of a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1971
ISSN: 0025-5645
DOI: 10.2969/jmsj/02310123