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Deo, Satya
- Boundedly Metacompact or Finitistic Spaces and the Star Order of Covers
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Authors
Satya Deo
1,
David Gauld
2
Affiliations
1 Harish-Chandra Research Institute, Chhatnag Road, Jhusi Allahabad 211019, IN
2 The Department of Mathematics, The University of Auckland Private Bag 92019, Auckland, NZ
1 Harish-Chandra Research Institute, Chhatnag Road, Jhusi Allahabad 211019, IN
2 The Department of Mathematics, The University of Auckland Private Bag 92019, Auckland, NZ
Source
The Journal of the Indian Mathematical Society, Vol 83, No 1-2 (2016), Pagination: 43-59Abstract
In this paper we first show that the topological notion of boundedly metacompact (first named finitistic) is equivalent to metris - ability for a topological manifold, and then we study the related notions. In particular, we study the star order of covers of a space. This leads us to propose a definition of dimension which we call star covering dimension.Keywords
Finitistic, Boundedly Metacompact, Boundedly Paracompact, Star Order.
References
- Glen E. Bredon, Introduction to Compact Transformation Groups, Academic Press, 1972.
- Satya Deo and A. R. Pears, Completely finitistic spaces are finite dimensional. Bull. London Math. Soc., 17(1985), 49–51.
- Satya Deo and H. S. Tripathi, Compact Lie Group actions on finitistic spaces, Topology, 21(1982), 391–399.
- Dennis K. Burke, Covering Properties, in K Kunen and J Vaughan, eds, "Handbook of Set-Theoretic Topology," Elsevier, 1984, 347–422.
- C. H. Dowker, Mapping Theorems for Non-compact Spaces, Amer. J. Math., 69(1947), 200–242.
- P. Fletcher, R. A. McCoy and R. Slover, On Boundedly Metacompact and Boundedly Paracompact Spaces, Proc. Amer. Math. Soc., 25(1970), 335–342.
- David Gauld, Non-metrisable Manifolds, Springer, 2014.
- James R. Munkres, Topology, a First Course, Prentice-Hall, 1975.
- Peter Nyikos, The Theory of Nonmetrizable Manifolds, in K Kunen and J Vaughan, eds, “Handbook of Set-Theoretic Topology,”Elsevier, 1984, 634–684.
- A. R. Pears, Dimension Theory of General Spaces, Cambridge University Press, 1975.
- R. G. Swan, A new method in fixed point theory, Comment. Math. Helv. 34(1960), 1–16.
- Strongly Contractible Polyhedra which are Not Simply Contractible at n Points For any n≥ 2
Abstract Views :173 |
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Authors
Affiliations
1 Harish-Chandra Research Institute (HRI), Chhatnag Road, Jhunsi, Allahabad-211 019, IN
1 Harish-Chandra Research Institute (HRI), Chhatnag Road, Jhunsi, Allahabad-211 019, IN
Source
The Journal of the Indian Mathematical Society, Vol 72, No 1-4 (2005), Pagination: 75-82Abstract
In this paper we study the concept of strict contractibility defined by E. Michael and construct an example stated in the title of the paper. We also give examples of compact metric spaces in Euclidean 3-space which are simply contractible at n points, for any n ≥ 1, but are not strongly contractible at those points.- Invariance of Dimension of Multivariate Spline Spaces
Abstract Views :176 |
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Authors
Affiliations
1 Department of Mathematics and Computer Science, R.D. University, Jabalpur 482001, IN
1 Department of Mathematics and Computer Science, R.D. University, Jabalpur 482001, IN
Source
The Journal of the Indian Mathematical Society, Vol 60, No 1-4 (1994), Pagination: 71-81Abstract
Let X be a compact polyhedron embedded in the Euclidean space Rd, d≥1, and Δ be a triangulation of X. In practical applications one always considers those connected polyhedra X which admit a pure triangulation Δ, i.e., all maximal simplexes of Δ are d-dimensional.- Index of a Finitistic Space and a Generalization of the Topological Central Point Theorem
Abstract Views :152 |
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Authors
Affiliations
1 NASI Senior Scientist, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, IN
1 NASI Senior Scientist, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 28, No 2 (2013), Pagination: 223–232Abstract
In this paper we prove that if G is a p-torus (resp. torus) group acting without fixed points on a finitistic space X (resp. with finitely many orbit types), then the G-index iG(X) < ∞. Using this G-index we obtain a generalization of the Central Point Theorem and also of the Tverberg Theorem for any d-dimensional Hausdorff space.- Hopfian and Co-Hopfian Zero-Dimensional Spaces
Abstract Views :153 |
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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.