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Topological Spaces Analysis


Affiliations
1 Department of S & H, Gopal Reddy College of Engineering & Technology, India
     

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In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods. A topological space is the most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. Other spaces, such as Euclidean spaces, metric spaces and manifolds, are topological spaces with extra structures, properties or constraints. Although very general, topological spaces are a fundamental concept used in virtually every branch of modern mathematics. The branch of mathematics that studies topological spaces in their own right is called point-set topology or general topology.

Keywords

Nano Technology, Topology Structure, Approximation Space.
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  • Topological Spaces Analysis

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Authors

A. Kunasamy
Department of S & H, Gopal Reddy College of Engineering & Technology, India
S. Kannaki
Department of S & H, Gopal Reddy College of Engineering & Technology, India

Abstract


In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods. A topological space is the most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. Other spaces, such as Euclidean spaces, metric spaces and manifolds, are topological spaces with extra structures, properties or constraints. Although very general, topological spaces are a fundamental concept used in virtually every branch of modern mathematics. The branch of mathematics that studies topological spaces in their own right is called point-set topology or general topology.

Keywords


Nano Technology, Topology Structure, Approximation Space.

References