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Varadarajan, K.
- Generalised Gottlieb Groups
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Authors
Affiliations
1 Tata Institute of Fundamental Research, IN
1 Tata Institute of Fundamental Research, IN
Source
The Journal of the Indian Mathematical Society, Vol 33, No 2-4 (1969), Pagination: 141-164Abstract
In his paper "A certain subgroup of the fundamental group" [4] D. A. Gottlieb introduced a certain subgroup G{X, x0) of the fundamental group n1(X,x0) for every connected CW-complex X and studied the properties of this subgroup.- Hopfian and Co-Hopfian Zero-Dimensional Spaces
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Authors
Satya Deo
1,
K. Varadarajan
2
Affiliations
1 Department of Mathematics and Computer Science, R.D. University, Jabalpur-482001, IN
2 Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta Canada T2N IN4, CA
1 Department of Mathematics and Computer Science, R.D. University, Jabalpur-482001, IN
2 Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta Canada T2N IN4, CA
Source
Journal of the Ramanujan Mathematical Society, Vol 9, No 2 (1994), Pagination: 177-202Abstract
The main results proved in this paper are:
(i) The only Hopfian or co-Hopfian objects among compact totally disconnected metrizable spaces are finite discrete spaces.
(ii) Every infinite closed subspace of (IN and hence any infinite closed subspace of N* = βN- N is non-co-Hopfian. However, N* admits an abundance of non-closed subspaces which are simultaneously Hopfian and co-Hopfian.
(iii) There are at least 2C non-homeomorphic compact totally disconnected perfect co-Hopfian spaces which are not rigid.
Keywords
Rigid Spaces, Rigid Spaces for a Class of Maps, Hopfian and Co-Hopfian Spaces, Continuous Displacements. F-Spaccs, Growth of a Space, Extremally Disconnected Spaces.- Residual Finiteness in Rings and Modules
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Authors
Affiliations
1 University of Calgary, Calgary Albert A, Canada T2N 1N4, CA
1 University of Calgary, Calgary Albert A, Canada T2N 1N4, CA