On some fundamental problems in cluster set theory

Eidswick, J. A.

doi:10.1090/S0002-9939-1973-0313454-X

On some fundamental problems in cluster set theory
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by J. A. Eidswick PDF

Proc. Amer. Math. Soc. 39 (1973), 163-168 Request permission

Abstract:

An attempt to characterize the local behavior of arbitrary functions of two real variables in terms of their cluster sets along various approach curves leads to two main problems: (1) Finding a “small” family ${\Gamma _0}$ of approach curves such that cluster sets along ${\Gamma _0}$ determine total cluster sets; (2) Finding a “large” family of approach curves along which cluster sets can be preassigned. A nice solution of (1) is found and (2) is partially solved. Conjectures are made concerning a link between (2) and sets which are always of the first category.

References

Sui punti di discontinuita delle funzioni di variabile reale

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