## Finely differentiable monogenic functions

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*Roman Lavicka*

**Address.**

Mathematical Institute, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic

**E-mail. **

lavicka@karlin.mff.cuni.cz

**Abstract.**

Since 1970's B. Fuglede and others have been studying finely holomorhic functions, i.e., `holomorphic' functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in \cite{lav2} like a higher dimensional analogue of finely holomorphic functions.