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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.2 No.1

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BASIS FOR ALMOST LINEAR SPACES

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
1995, v.2 no.1, pp.43-51
Lee, Sang-Han (Chungbuk National University)
Lee, Sang-Han. (1995). BASIS FOR ALMOST LINEAR SPACES, 2(1), 43-51.

Abstract

In this paper, we introduce the almost linear spaces, a generalization of linear spaces. We prove that if the almost linear space X has a finite basis then, as in the case of a linear space, the cardinality of bases for the almost linear space X is unique. In the case X = Wx ＋ Vx, we prove that B'= {$\chi$'$_1,...,x'_n} is a basis for the algebraic dual X$^#$ of X if B = {$\chi$'$_1,...,x'_n} is a basis for the almost linear space X. And we have an example X($\neq$Wx ＋ Vx) which has no such a basis.

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한국수학교육학회지시리즈B:순수및응용수학

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