Asymptotic values and Baire category

Author:
Chaim Mida

Journal:
Proc. Amer. Math. Soc. **41** (1973), 492-494

MSC:
Primary 30A72

DOI:
https://doi.org/10.1090/S0002-9939-1973-0324046-0

MathSciNet review:
0324046

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Abstract: Let be meromorphic in the unit disc, and let be a complex number. Given , let denote the set of points for which the cluster set lies in the -neighbourhood of for some arc . Then a sufficient condition that the set of points on the unit circle at which possesses point-asymptotic value be of first category is that contains no arc for some .

**[1]**E. F. Collingwood and A. J. Lohwater,*The theory of cluster sets*, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR**0231999****[2]**A. J. Lohwater,*Some function-theoretic results involving Baire category*, Topics in analysis (Colloq. Math. Anal., Jyväskylä, 1970) Springer, Berlin, 1974, pp. 253–259. Lecture Notes in Math., Vol. 419. MR**0377060****[3]**E. C. Titchmarsh,*Han-shu lun*, Translated from the English by Wu Chin, Science Press, Peking, 1964 (Chinese). MR**0197687****[4]**Gordon Thomas Whyburn,*Analytic Topology*, American Mathematical Society Colloquium Publications, v. 28, American Mathematical Society, New York, 1942. MR**0007095**

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0324046-0

Article copyright:
© Copyright 1973
American Mathematical Society