Algebraic characterisation of hyperspace corresponding to topological vector space
محل انتشار: مجله ابرساختارها، دوره: 11، شماره: 1
سال انتشار: 1401
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 66
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شناسه ملی سند علمی:
JR_JHSMS-11-1_004
تاریخ نمایه سازی: 16 بهمن 1402
چکیده مقاله:
Let X be a Hausdorff topological vector space over the field of real or complex numbers. When Vietoris topology is given, the hyperspace \com {\mathcal X}{} of all nonempty compact subsets of X forms a topological exponential vector space over the same field. Exponential vector space [shortly, evs] is an algebraic ordered extension of vector space in the sense that every evs contains a vector space, and conversely, every vector space can be embedded into such a structure. A semigroup structure, a scalar multiplication and a partial order with some compatible topology comprise the topological evs structure. In this study, we have shown that besides \com {\mathcal X}{}, there are other hyperspaces namely \set{\mathcal X}{}, \set{\mathcal X}{Bal} \set{\mathcal X}{CV}, \set{\mathcal X}{N_\theta}, \set{\X}{S}, \set{\mathcal X}{\theta} which have the same structure. To characterise the hyperspaces \set{\mathcal X}{}, \com {\mathcal X}{} in light of evs, we have introduced some properties of evs which remain invariant under order-isomorphism. We have also introduced the concept of primitive function of an evs, which plays an important role in such characterisation. Lastly, with the help of these properties, we have characterised \com {\mathcal X}{} as well as \set{\mathcal X}{} as exponential vector spaces.
کلیدواژه ها:
Exponential vector space ، topological exponential vector space ، hyperspaces ، order-isomorphism ، primitive function
نویسندگان
Jayeeta Saha
Department of Mathematics, Vivekananda College,Thakurpukur, Kolkata, West Bengal, India
Sandip Jana
Department of Pure Mathematics, University of Calcutta, Kolkata, West Bengal, India