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Thin Set (analysis)
In mathematical analysis, a thin set is a subset of ''n''-dimensional Complex coordinate space, complex space C''n'' with the property that each point has a neighbourhood (topology), neighbourhood on which some non-zero holomorphic function vanishes. Since the set on which a holomorphic function vanishes is closed set, closed and has empty Interior (topology), interior (by the Identity theorem), a thin set is nowhere dense, and the Closure (topology), closure of a thin set is also thin. The Fine topology (potential theory), fine topology was introduced in 1940 by Henri Cartan to aid in the study of thin sets. References * {{mathanalysis-stub Several complex variables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
