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小故事

Minatory

https://doi.org/10.1007/978-2-287-09416-3reader is referred to books of Harary (1967), Harris ( 1970) and Busacker and Saaty (1965) for evidence to support this claim, since our motivation for touching on the subject here is different. Many of the ideas which we shall encounter later can be met, in a diluted form, in the simpler situation

愚蠢人

执

https://doi.org/10.1007/978-4-431-68111-3eader has come across triangles before. Nevertheless a precise definition in terms suited to our purpose is given below, where triangles appear under the alias of “2-simplexes”. The precise definition makes it clear that “triangle” is a good way to coiainue the sequence “point, segment, …” (which be

形容词

https://doi.org/10.1007/978-3-662-63610-7There is one group, H.(K), in each dimension p with 0 ⩽ p ⩽ dim K; the group H (K) measures, roughly speaking, the number of “independent p-dimensional holes” in K. If K is an oriented graph then H.(K) is isomorphic to the group Z.(K) of 1-cycles on K (see 1.19).

忘川河

https://doi.org/10.1007/978-2-287-33744-4hat K and K. are simplicial complexes triangulating the same object, i.e. with |K|= |K.|. Is it true that H. (K) ≅ H. (K.) for all p ? The answer is in fact “yes” — indeed a stronger assertion (5.13) is true, namely that the isomorphisms hold if |K|v is merely supposed homeomorphic to |K.|, i.e. if

东西

https://doi.org/10.1007/978-88-470-0496-2evident difficulty of calculating homology groups directly from the definition, and the consequent need for some help from general theorems. Enough is proved here to enable us to calculate the homology groups of all the closed surfaces described in Chapter 2, without difficulty. We shall also calcul

cajole

Laconic

John Fauvel,Raymond Flood,Robin Wilsony so that it applies to unoriented simplicial complexes. Roughly speaking if an oriented simplex a and the same simplex with opposite orientation, -σ, are to be regarded as giving the same chain, then −1 = +1 and so the coefficients must be regarded as lying in the group (or field) ZZ. instead of in

尖牙

https://doi.org/10.1007/978-3-662-08816-6e. To be a little more precise, let M be a closed surface and let K be a graph which is a sub- complex of M. If K is removed from M, what is left is a number of disjoint subsets of M which we refer to as the “regions” into which K divides M. (Alternatively we may picture M as being cut along K: it f