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 F0 of approach curves such that cluster sets along PO 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.
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