11 papers
Persistence diagrams of finite topological spaces
Akhilesh Badra, Hemant Kumar Singh
In this paper, we apply persistent homology to study finite topological spaces by associating persistence diagrams with their elements through the furtherness function. This approa…
Furtherness in finite topological spaces
Akhilesh Badra, Hemant Kumar Singh
In this paper, we introduce a novel distance-like notion of furtherness for finite topological spaces, demonstrating that every finite space can be viewed as an asymmetric pseudome…
Free Circle Actions on the Product of Three Spheres
Dimpi, Hemant Kumar Singh
The orbit spaces of free S^0-actions on the mod 2 cohomology product of three spheres, S^n x S^m x S^l, 1 <= n <= m <= l have been determined in [6]. In this paper, we extend these…
Center and radius of a subset of metric space
Akhilesh Badra, Hemant Kumar Singh
In this paper, we introduce a notion of the center and radius of a subset A of metric space X. In the Euclidean spaces, this notion can be seen as the extension of the center and r…
Fixed Point Sets of Involutions on the Product of Three Spheres
Dimpi, Hemant Kumar Singh
Let G = Z2 act on a finitistic space X having mod 2 cohomology of the product of three spheres S^n x S^m x S^l. In this paper, we have determined the fixed point sets of involution…
Finitistic Spaces with the Orbit Space FP^n x S^m
Anju Kumari, Hemant Kumar Singh
Let G = S^d, d = 0, 1 or 3, act freely on a finitistic connected space X. This paper gives the cohomology classification of X if a mod 2 or rational cohomology of the orbit space X…
Finitistic Spaces with Orbit Space a Product of Projective Spaces
Anju Kumari, Hemant Kumar Singh
Let G = Z2 act freely on a nitistic space X. If the mod 2 cohomology of X is isomorphic to the real projective space RP^{2n+1} (resp. complex projective space CP^{2n+1}) then the m…
Involutions on the product of Quaternionic Projective space and Sphere
Dimpi, Hemant Kumar Singh
Let G = Z2 act on a finite CW-complex X having mod 2 cohomology isomorphic to the product of quaternionic projective space and sphere HPn x Sm, n, m > or = 1. This paper is concern…
Fixed point sets and orbit spaces of wedge of three spheres
Dimpi, Hemant Kumar Singh
Let be a finite CW-complex having mod cohomology isomorphic to a wedge of three spheres . The aim o…
Involution on the product of projective space and sphere
Dimpi, Hemant Kumar Singh
Let act on a finite CW-complex having mod 2 cohomology isomorphic to the product of projective space and sphere where $\mat…
Orbit spaces of free involutions on the product of three spheres
Dimpi, Hemant Kumar Singh
In this paper, we have determined the orbit spaces of free involutions on a finitistic space having mod 2 cohomology of the product of three spheres $\mathbb{S}^n\times \mathbb{S}^…