Volume 10, 1998

University of Bialystok

Copyright (c) 1998 Association of Mizar Users

**Yatsuka Nakamura**- Shinshu University, Nagano

- We define a graph on an abstract set, edges of which are pairs of any two elements. For any finite sequence of a plane, we give a definition of nodic, which means that edges by a finite sequence are crossed only at terminals. If the first point and the last point of a finite sequence differs, simpleness as a chain and nodic condition imply unfoldedness and s.n.c. condition. We generalize Goboard Theorem, proved by us before, to a continuous case. We call this Fashoda Meet Theorem, which was taken from Fashoda incident of 100 years ago.

- A Graph by Cartesian Product
- Shortcuts of Finite Sequences in Plane
- Norm of Points in ${\calE}^{n}_{\rmT}$
- Extended Goboard Theorem and Fashoda Meet Theorem

- [1]
Grzegorz Bancerek.
Cardinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Grzegorz Bancerek.
The ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Jozef Bialas and Yatsuka Nakamura.
The theorem of Weierstrass.
*Journal of Formalized Mathematics*, 7, 1995. - [6]
Leszek Borys.
Paracompact and metrizable spaces.
*Journal of Formalized Mathematics*, 3, 1991. - [7]
Czeslaw Bylinski.
Basic functions and operations on functions.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Czeslaw Bylinski.
The sum and product of finite sequences of real numbers.
*Journal of Formalized Mathematics*, 2, 1990. - [13]
Czeslaw Bylinski and Piotr Rudnicki.
Bounding boxes for compact sets in $\calE^2$.
*Journal of Formalized Mathematics*, 9, 1997. - [14]
Agata Darmochwal.
Compact spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Agata Darmochwal.
Families of subsets, subspaces and mappings in topological spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [16]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Agata Darmochwal.
The Euclidean space.
*Journal of Formalized Mathematics*, 3, 1991. - [18]
Agata Darmochwal and Yatsuka Nakamura.
Metric spaces as topological spaces --- fundamental concepts.
*Journal of Formalized Mathematics*, 3, 1991. - [19]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs.
*Journal of Formalized Mathematics*, 3, 1991. - [20]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Krzysztof Hryniewiecki.
Graphs.
*Journal of Formalized Mathematics*, 2, 1990. - [22]
Stanislawa Kanas, Adam Lecko, and Mariusz Startek.
Metric spaces.
*Journal of Formalized Mathematics*, 2, 1990. - [23]
Jaroslaw Kotowicz and Yatsuka Nakamura.
Go-Board theorem.
*Journal of Formalized Mathematics*, 4, 1992. - [24]
Jaroslaw Kotowicz and Yatsuka Nakamura.
Introduction to Go-Board --- part I.
*Journal of Formalized Mathematics*, 4, 1992. - [25]
Yatsuka Nakamura and Piotr Rudnicki.
Vertex sequences induced by chains.
*Journal of Formalized Mathematics*, 7, 1995. - [26]
Yatsuka Nakamura and Piotr Rudnicki.
Oriented chains.
*Journal of Formalized Mathematics*, 10, 1998. - [27]
Yatsuka Nakamura and Andrzej Trybulec.
Decomposing a Go-Board into cells.
*Journal of Formalized Mathematics*, 7, 1995. - [28]
Takaya Nishiyama and Yasuho Mizuhara.
Binary arithmetics.
*Journal of Formalized Mathematics*, 5, 1993. - [29]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [30]
Jan Popiolek.
Some properties of functions modul and signum.
*Journal of Formalized Mathematics*, 1, 1989. - [31]
Agnieszka Sakowicz, Jaroslaw Gryko, and Adam Grabowski.
Sequences in $\calE^N_\rmT$.
*Journal of Formalized Mathematics*, 6, 1994. - [32]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [33]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [34]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
*Journal of Formalized Mathematics*, 1, 1989. - [35]
Wojciech A. Trybulec.
Pigeon hole principle.
*Journal of Formalized Mathematics*, 2, 1990. - [36]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [37]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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