# Arithmetic Operations on Functions from Sets into Functional Sets

Formalized Mathematics (2009)

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

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topArtur 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

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

## Citations in EuDML Documents

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

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