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K. Varadarajan ¹, K. Madhavan Nair ¹

Affiliations
1 Oil and Natural Gas Commission, Madras-17, IN

Abstract

The NW-SE to WNW-ESE trending faults, having an oblique trend to the Western Ghats have played a significant role in the structural evolution of the basin and have also controlled the facies distribution and stratigraphy of the different units. The recent reactivation of the NNW-SSE to N-S trending faults which are presumbly associated with the uplift of the Western Ghats, appear to be responsible for the foundering of the greater part of the offshore basin and for shaping the present day coastline with lateritic terraces. Evidences also indicate that the NE-SW trending fractures have been reactivated recently, affecting even the Quaternary sedimentary cover.

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K. Varadarajan ¹

Affiliations
1 Tata Institute of Fundamental Research, IN

Abstract

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.

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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

Abstract

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.

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K. Varadarajan ¹

Affiliations
1 University of Calgary, Calgary Albert A, Canada T2N 1N4, CA

Abstract

In [5] J. Lewin showed that there are many similarities between finitely generated (abbreviated as f(g) groups and/ g rings. Based on the work of J. Lewin, in [8] M. Orzech and L. Ribcs obtained many interesting results on residual finiteness and Hopficity in the category of rings. In our present paper, we give some more instances of similarities between/ g groups and/ g rings. Also, we study residual finiteness and Hopficity in module categories. This study has led us to extending the scope of the work of the above mentioned authors.

Keywords

Residual Finiteness, Hopficity, Subrings, Ideals, Boolean Rings.

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