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# Quasi Set Topological Vector Subspaces

## By Smarandache, Florentin

Book Id: WPLBN0002828546
Format Type: PDF (eBook)
File Size: 4.08 mb
Reproduction Date: 8/6/2013

 Title: Quasi Set Topological Vector Subspaces Author: Smarandache, Florentin Volume: Language: English Subject: Collections: Historic Publication Date: 2013 Publisher: World Public Library Member Page: Florentin Smarandache Citation APA MLA Chicago Smarandache, F., & Vasantha Kandasamy, W. B. (2013). Quasi Set Topological Vector Subspaces. Retrieved from http://self.gutenberg.org/

Description
Chapter one is introductory in nature and chapter two uses vector spaces to build quasi set topological vector subspaces. Not only we use vector spaces but we also use S-vector spaces, set vector spaces, semigroup vector spaces and group vector spaces to build set topological vector subspaces. These also give several finite set topological spaces. Such study is carried out in chapters three and four.

Summary
In this book the authors introduce four types of topological vector subspaces. All topological vector subspaces are defined depending on a set. We define a quasi set topological vector subspace of a vector space depending on the subset S contained in the field F over which the vector space V is defined. These quasi set topological vector subspaces defined over a subset can be of finite or infinite dimension. An interesting feature about these spaces is that there can be several quasi set topological vector subspaces of a given vector space. This property helps one to construct several spaces with varying basic sets.

Excerpt
To every quasi set topological vector subspace T relative to the set P  F, we have a lattice associated with it we call this lattice as the Representative Quasi Set Topological Vector subspace lattice (RQTV-lattice) of T relative to P. When T is finite we have a nice representation of them. In case T is infinite we have a lattice which is of infinite order. We can in all cases give the atoms of the lattice which is in fact the basic set of T over P. It is pertinent to keep on record that the T and the basic set (or the atoms of the RQTV-lattice) depends on the set P over which it is defined. We will illustrate this situation by some examples.