On removing coincidences of two maps when only one, rather than both, of them may be deformed by a homotopy.
On removing coincidences of two maps when only one, rather than both, of them may be deformed by a homotopy.
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在消除两个映射的重合时，只有其中一个而不是两者都可以通过同伦变形。
DOI：
10.2140/pjm.1972.40.45
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发表时间：
1972
期刊：
影响因子：
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通讯作者：
R. Brooks
中科院分区：
文献类型：
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作者：
R. Brooks
已知，如果/，g: X - > Y是拓扑空间X到拓扑流形Y的映射，并且/和g可以被映射/ ‘和g的无重合同伦变形，则/可以被映射f ’的同伦变形，使得f和g是无重合的。这个结果推广如下：如果/，g: X -»Y是拓扑空间X到拓扑流形Y的映射，并且f和g′分别与/和g′同伦，那么对于任何从g到g\的同伦{gt}，存在一个从f到g\的同伦{ft}使得ft和g′-t的重合集对所有t e[0,1]都相同。给出了该结果在不动点理论和根理论中的一些应用。
It is known that if /, g: X —> Y are maps of a topological space X into a topological manifold Y, and that / and g can be deformed by homotopies to maps / ' and g which are coincidence-free, then / may be deformed by a homotopy to a map f" such that f and g are coincidence-free. This result is generalized as follows: If /, g: X—» Y are maps of a topological space X into a topological manifold Y and f and g' are homotopic to / and g respectively, then for any homotopy {gt} from g to g\ there is a homotopy {ft} from f such that the set of coincidences of ft and gι-t is the same for all t e [0,1]. Some applications of this result to fixed point theory and root theory are indicated.