منابع مشابه
On 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...
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The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...
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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...
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This theorem may be proved as an application of Stasheff's theory of yl „-spaces, and has certainly been noted by Stasheff. A method of proof was outlined in [3] in order to prove Corollary 3.12 of that paper, but the proof was defective.2 We give here a proof whose structure is essentially dual to that of the structure of the proof of Theorem A in [l], but which is much simpler in detail. Just...
متن کاملThe metric dimension and girth of graphs
A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1959
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1959.100378