Topology via Graph Ideals

P. Gnanchandra, K. Lalithambigai


The study of ideal topological space has started since 1933 and till date it is being developed by several mathematicians. Various classes of open sets, different types of operators and exploration of elementary topological results in ideal topological spaces have been discussed in various research papers. Methods of generating topologies using various relations have been explored by many researchers. Many researchers explored the methods of inducing topologies via graphs. This paper, introduces the notions of graph ideals, graph local function and characterizes some of their properties. It also describes a method of generating a new graph topology on the vertex set of a graph from the graph adjacency topology using Kuratowski closure operator and depicts the nature of open sets with respect to the new topology. Further, it explores the condition for compatibility of the graph adjacency topology with graph ideal.

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