Arithmetic Operations on Functions from Sets into Functional Sets

Artur Korniłowicz

Formalized Mathematics (2009)

  • Volume: 17, Issue: 1, page 43-60
  • ISSN: 1426-2630

Abstract

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In this paper we introduce sets containing number-valued functions. Different arithmetic operations on maps between any set and such functional sets are later defined.MML identifier: VALUED 2, version: 7.11.01 4.117.1046

How to cite

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Artur Korniłowicz. "Arithmetic Operations on Functions from Sets into Functional Sets." Formalized Mathematics 17.1 (2009): 43-60. <http://eudml.org/doc/267184>.

@article{ArturKorniłowicz2009,
abstract = {In this paper we introduce sets containing number-valued functions. Different arithmetic operations on maps between any set and such functional sets are later defined.MML identifier: VALUED 2, version: 7.11.01 4.117.1046},
author = {Artur Korniłowicz},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {43-60},
title = {Arithmetic Operations on Functions from Sets into Functional Sets},
url = {http://eudml.org/doc/267184},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Artur Korniłowicz
TI - Arithmetic Operations on Functions from Sets into Functional Sets
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 1
SP - 43
EP - 60
AB - In this paper we introduce sets containing number-valued functions. Different arithmetic operations on maps between any set and such functional sets are later defined.MML identifier: VALUED 2, version: 7.11.01 4.117.1046
LA - eng
UR - http://eudml.org/doc/267184
ER -

References

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  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  3. [3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  4. [4] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  5. [5] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990. 
  6. [6] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990. 
  7. [7] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003. 
  8. [8] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. 
  9. [9] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  10. [10] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  11. [11] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 

Citations in EuDML Documents

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  1. Artur Korniłowicz, The Correspondence Between n -dimensional Euclidean Space and the Product of n Real Lines
  2. Artur Korniłowicz, On the Continuity of Some Functions
  3. Keiko Narita, Artur Kornilowicz, Yasunari Shidama, More on the Continuity of Real Functions
  4. Artur Korniłowicz, Marco Riccardi, The Borsuk-Ulam Theorem
  5. Karol Pąk, Tietze Extension Theorem for n-dimensional Spaces
  6. Karol Pąk, Flexary Operations
  7. Karol Pąk, Brouwer Invariance of Domain Theorem
  8. Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama, Contracting Mapping on Normed Linear Space

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