Multivalued linear transformations of hyperspaces

Authors

  • R. Ameri School of Mathematics, Statistic and Computer Sciences, College of Science, University of Tehran,Tehran, Iran
  • R. A. Borzooei Department of Mathematics, Shahid Beheshti University, Tehran, Iran,
  • K. Ghadimi Department of Mathematics, Payame Noor University, Tehran, Iran

DOI:

https://doi.org/10.23755/rm.v27i1.31

Keywords:

hypervector space, multivalued linear transforma- tion, category, fundamental relation

Abstract

The purpose of this paper is the study of multivalued linear transformations of hypervector spaces (or hyperspaces) in the sense of Tallini. In this regards first we introduce and study various multivalued linear transformations of hyperspaces and then constitute the categories of hyperspaces with respect the different linear transformations of hyperspaces as the morphisms in these categories. Also, we construct some algebraic hyperoperations on Hom K (V,W), the set of all multivalued linear transformations from a hyperspace V into hyperspaces W, and obtaine their basic properties. Finally, we construct the fundamental functor F from HV K , category of hyperspaces over field K into V K , the category of clasical vector space over K.

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Published

2014-12-14

Issue

Vol. 27 (2014)

Section

Volume 27-2014

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