Conditions under which disks are liftable
Author:
Edythe P. Woodruff
Journal:
Trans. Amer. Math. Soc. 186 (1973), 403418
MSC:
Primary 57A10; Secondary 54B15
MathSciNet review:
0328943
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Abstract: A generalization of the concept of lifting of an ncell is studied. In the usual upper semicontinuous decomposition terminology, let S be a space, be the decomposition space, and the projection mapping be . A set is said to be a Plift of a set if is homeomorphic to X and is X. Examples are given in which the union of two Pliftable sets does not Plift. We prove that if compact 2manifolds A and B each Plift, their union is a disk in , their intersection misses the singular points of the projection mapping, and the intersection of the singular points with the union of A and B is a 0dimensional set, then the union of A and B does Plift. Even if a disk D does not Plift, it is proven that for there is a Pliftable disk homeomorphic to D, provided that the given decomposition of is either definable by 3cells, or the set of nondegenerate elements is countable and is homeomorphic to . With further restrictions on the decomposition, this Pliftable disk can be chosen in such a manner that it agrees with D on the singular points of D.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197303289436
PII:
S 00029947(1973)03289436
Keywords:
Decomposition space,
topology of ,
lift of a space,
Plift,
monotone decomposition,
cellular decomposition,
decomposition definable by 3cells,
tame,
neighborhoods of submanifolds
Article copyright:
© Copyright 1973 American Mathematical Society
