On Combinatorial Topology.
On Combinatorial Topology.
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关于组合拓扑。
DOI：
10.1073/pnas.18.1.86
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发表时间：
1932
影响因子：
11.1
通讯作者：
A. Tucker
中科院分区：
文献类型：
--
作者：
A. Tucker
本说明给出了一个初步帐户的一些功能的一份文件组合拓扑将出版更完整的详细资料在稍后的日期。术语和符号是仿照莱夫谢茨的，但我们要处理的细胞{EpI是迈耶考虑的抽象类型。2. Lefschetz（同上）描述了使用一般类型的单元的优点，其中入射数77可以具有任何整数值。在前引，pp. 104-5）。但有一个困难，即，从Ep +1的链边界上抵消的Ep与不在Ep+ 1的边界上的Ep根本没有区别（组合地）。这可以通过引入一个关系来克服，该关系告诉Ep何时在Ei（p< q）的边界上。这种定性关系与关联数的定量关系的唯一联系是：如果Ep不在Ep + 1的边界上，则关联数为0。1.开放式和封闭式子复合体。复形K是一组胞元，使得边界链的边界链总是0，即，
This note gives a preliminary account of some features of a paper on combinatorial topology to be published in more complete detail at a later date. The terminology and notation are patterned after that of Lefschetz, 1 but the cells {EpI with which we shall deal are of the abstract type considered by Mayer. 2 Theadvantage of using a general type of cell where theincidence numbers 77 may have any integral values, is described by Lefschetz (loc. cit., pp. 104-5). But there is one difficulty, viz., an Ep cancelling out of the chain-boundary of an Ep+ i is not (combinatorially) distinguished from an Ep not on theboundary of Ep+ 1 at all. This can be overcome by introducing a relation telling when an Ep is on the boundary of an E,(p< q). The only connection of this quali-tative relation with the quantitative one of incidence numbers is that ifEp is not on the boundary ofEp+ 1 the incidence number is 0. 1. Open and Closed Sub-Complexes.-A complex K is a set of cells such that the boundary-chain of a boundary-chain is always 0, ie,