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Titlebook: Studies in Pure Mathematics; To the Memory of Pau Paul Erdős,László Alpár,András Sárközy Book 1983 Springer Basel AG 1983 algebra.analytic

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Syntopogenous spaces and zero-set spaces,asi-uniform spaces and uniform spaces. Zero-set spaces have been introduced in [5] as a generalization of the structure composed of a set equipped with a topology and of the system of all zero-sets of real-valued functions continuous with respect to this topology.
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The spherical derivative of meromorphic functions with relatively few poles,Suppose that .(.) is a function meromorphic in the plane ℂ and let.denote the spherical derivative of .(.). For r>0 we set
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A Blaschke product with a level-set of infinite length,A recent paper by . and A. . [1] describes an outer function . in the unit disk . such that, for uncountably many values ., the .-level-set {z:|.(.)| = .} has infinite length. We shall now show that an inner function can also have a level-set of infinite length.
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,On an open problem of Paul Turán concerning 3-graphs,The third of .. 1961 list of . [4] reads:
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On a problem of Lehmer,D. H. . [6] asked whether for every ε>0 there exists a monic polynomial . ∈ .[.] such that
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On extrermal polynomials,Let ℘ be the set of polynomials of the form.where ...... are nonnegative integers, and the coefficients .. (.=0,1,...,..) are real (the complex case will be commented later). For the sake of convenience we set
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