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Cluster sets of arbitrary functions defined on plane sets. (English) Zbl 0343.04002

MSC:

03E15 Descriptive set theory
30D40 Cluster sets, prime ends, boundary behavior
26A03 Foundations: limits and generalizations, elementary topology of the line
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References:

[1] F. Bagemihl: Ambiguous points of arbitrary planar sets and functions. Zeitschr. f. math. Logik und Grundlagen d. Math. Bd. 12, S. 205-217 (1966). · Zbl 0149.01704
[2] F. Bagemihl: Curvilinear cluster sets of arbitrary functions. Proc. Nat. Acad. Sci. 41 , 379-382 (1955). · Zbl 0065.06604
[3] F. Bagemihl, P. Humke: Rectifiably ambiguous points of planar sets. J. Australian Math. Soc. Vol. XX-(Series)-part l, pp. 85-109 (1975). · Zbl 0305.04005
[4] H. Hahn: Reelle Funktionen. Leipzig, 1932. · Zbl 0005.38903
[5] P. Humke: Samely ambiguous points of arbitrary planar sets and functions. Zeitsch. f. math. Logik und Grundlagen d. Math. Bd. 19, S. 427-433 (1973). · Zbl 0307.04003
[6] P. Humke: An example of a function with multiple ambiguities. Zeitschr. f. math. Logik und Grundlagen d. Math. Bd. 21, S. 413-416 (1975). · Zbl 0318.26003
[7] J. E. McMillan: Arbitrary functions defined on plane sets. Michigan Math. J. 14, 445 - 447 (1967). · Zbl 0206.51701
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