Recognizing certain factors of

Author:
Leonard R. Rubin

Journal:
Proc. Amer. Math. Soc. **26** (1970), 199-200

MSC:
Primary 54.78

DOI:
https://doi.org/10.1090/S0002-9939-1970-0266180-7

MathSciNet review:
0266180

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Abstract: It has been proved that for certain peculiar decomposition spaces of euclidean -space is homeomorphic to euclidean -space, . In this paper we prove that if a decomposition space of is generated by a trivial defining sequence whose elements are cubes with handles, and this sequence can be replaced by a toroidal defining sequence, then is homeomorphic to .

**[1]**J. J. Andrews and Leonard Rubin,*Some spaces whose product with is*, Bull. Amer. Math. Soc.**71**(1965), 675-677. MR**31**#726. MR**0176454 (31:726)****[2]**R. H. Bing,*The cartesian product of a certain nonmanifold and a line is*, Ann. of Math. (2)**70**(1959), 399-412. MR**21**#5953. MR**0107228 (21:5953)****[3]**Leonard Rubin,*The product of an unusual decomposition space with a line is*, Duke Math. J.**33**(1966), 323-329. MR**33**#3283. MR**0195078 (33:3283)****[4]**Leonard R. Rubin,*The product of any dogbone space with a line is*, Duke Math. J.**37**(1970), 189-192. MR**0267548 (42:2450)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1970-0266180-7

Keywords:
Defining sequence,
toroidal sequence,
trivial sequence,
cubes with handles

Article copyright:
© Copyright 1970
American Mathematical Society