Volume 8, 1996

University of Bialystok

Copyright (c) 1996 Association of Mizar Users

**Yatsuka Nakamura**- Shinshu University, Nagano
**Roman Matuszewski**- Warsaw University, Bialystok

- We discuss here some methods for reconstructing special sequences which generate special polygonal arcs in ${\cal E}^{2}_{\rm T}$. For such reconstructions we introduce a ``mid" function which cuts out the middle part of a sequence; the ``$\downharpoonleft$" function, which cuts down the left part of a sequence at some point; the ``$\downharpoonright$" function for cutting down the right part at some point; and the ``$\downharpoonleft \downharpoonright$" function for cutting down both sides at two given points.\par We also introduce some methods glueing two special sequences. By such cutting and glueing methods, the speciality of sequences (generatability of special polygonal arcs) is shown to be preserved.

The work has been done while the second author was visiting Nagano in autumn 1996.

- Preliminaries
- Middle Function for Finite Sequences
- A Concept of Index for Finite Sequences in ${\cal E}^{2}_{\rm T}$
- Left and Right Cutting Functions for Finite Sequences in ${\cal E}^{2}_{\rm T}$
- Cutting Both Sides of a Finite Sequence and a Discussion of Speciality of Sequences in ${\cal E}^{2}_{\rm T}$

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