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such that, for every pair of a spanning tree in the graph and a complementary spanning tree in the dual graph, at least one of the two trees has distances...

Banach space (pronounced [ˈbanax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector...

several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of G are...

the topology of uniform convergence on bounded sets Strong topology (polar topology) – Continuous dual space endowed with the topology of uniform convergence...

the dimension of V {\displaystyle V} ), the dual set of B {\displaystyle B} is a set B ∗ {\displaystyle B^{*}} of vectors in the dual space V ∗ {\displaystyle...

problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its dual problem of intersecting...

of any proper subset of S. If S is a spanning set of a projective space P, then there is a subset of S that spans P and is projectively independent (this...

cycle space of a graph is the collection of its Eulerian spanning subgraphs. If one applies any set operation such as union or intersection of sets to two...

condition, where the dual space is endowed with the topology of uniform convergence on totally bounded sets. Montel space: a barrelled space where every closed...

theory of lattices, the dual lattice is a construction analogous to that of a dual vector space. In certain respects, the geometry of the dual lattice of a...

Fréchet, establishes an important connection between a Hilbert space and its continuous dual space. If the underlying field is the real numbers, the two are...

may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles formed by the combination of a path in the tree and...

combination of elements of S is to take zero for every coefficient ai. A set of vectors that spans a vector space is called a spanning set or generating set. If...

the continuous dual space is the zero space. In the case of the counting measure on the natural numbers (producing the sequence space L p ( μ ) = ℓ p...

instead. Let V be a real vector space of dimension n and V∗ its dual space. Now consider the direct sum W = V ⊕ V∗ of these spaces equipped with the following...

sets: Remove the current wall. Join the sets of the formerly divided cells. There are several data structures that can be used to model the sets of cells...

topological closure operator on a set gives rise to a topological space whose closed sets are exactly the closed sets with respect to the closure operator...

also topology, whence they originate. The notion dual to a filter is an order ideal. Special cases of filters include ultrafilters, which are filters that...

produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge. For example, in an oriented 3-dimensional Euclidean space, an oriented plane...

reciprocal space or k space, which is the dual of physical space considered as a vector space, and the reciprocal lattice is the sublattice of that space that...