Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Real Functions Spaces

Henryk Oryszczyszyn

Warsaw University, Bialystok

Krzysztof Prazmowski

Warsaw University, Bialystok
Summary.

This abstract contains a construction of the domain of functions defined in
an arbitrary nonempty set, with values being real numbers. In every such
set of functions we introduce several algebraic operations, which yield in
this set the structures of a real linear space, of a ring, and of a real
algebra. Formal definitions of such concepts are given.
Supported by RPBP.III24.C2.
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[4]
[13]
[11]
[14]
[2]
[3]
[1]
[8]
[7]
[12]
[5]
[6]
[10]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [10]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
Journal of Formalized Mathematics,
2, 1990.
 [11]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [12]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received March 23, 1990
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