Applications of Binary Intuitionistic Fine Topological Spaces for Digital Plane

A. G. Rose Venish; L. Vidyarani; M. Vigneshwaran

doi:10.26713/cma.v15i2.2655

Authors

A. G. Rose Venish Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education For Women, Coimbatore 641043, Tamil Nadu, India https://orcid.org/0000-0002-3710-997X (unauthenticated)
L. Vidyarani Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, Tamil Nadu, India https://orcid.org/0000-0002-2244-7140 (unauthenticated)
M. Vigneshwaran Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, Tamil Nadu, India https://orcid.org/0000-0003-1845-6877 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v15i2.2655

Keywords:

4 and 8-BIf T adjacencies, Digital plane, BIf TS, BIf -connected points

Abstract

In order to model computer images, digital spaces such as \(Z^{2}\) are utilized and the link between the classical topological spaces such as \(T_{1}, T_{1/2}, T_{0}\) spaces etc., and the digital spaces are studied by many authors to solve important connectivity problems, studying graphics, pattern recognition etc. In graph theoretical approach to solve connectivity contradictions 4 and 8 adjacencies serves as the basic. It is well known that key approaches to solve such problems are graph theoretic approach and topological approach. Traditional 4 and 8 adjacencies in a topology are considered in this article which aims to structure 4 and 8 adjacencies in a topology called binary intuitionistic fine topology \((\BI_fT)\). Initially 4 and 8 adjacencies-\(\BI_fT\) are constructed and operators such as 4 and 8-\(BI_fT\) interiors and closures are defined and their properties are discussed. Eventually, 4 and 8 connected-\(\BI_f\)-connected and non-connected points are defined and explained using example.

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