ISOMETRI PADA RUANG BERNORMA-n DAN RUANG BERNORMA-n NON-ARCHIMEDIAN; ISOMETRY ON n-NORMED SPACE AND NON-ARCHIMEDEAN n-NORMED SPACE

BURHANUDIN ARIF NURNUGROHO, Rini Indrati

2011 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

Mapping the norm . : X ? , can be expanded to become the norm-n, withX more than n-1 dimensional , and called the n-normed spaces. For n = 2, 2- normon 2-normed spaces, can be interpreted asbroad. While n-norm on nnormed space can be interpreted as the volume paralelpipedium. Valuation on a real field can be made specifically to the valuationof non-archimedian. Real normed space constructed by the vector space with the valuation of non- Archimedian field called non-Archimedian normed spaces. In thennormed spaces there are two concepts isometry, ie. n-isometry and weaknisometry. Further discussion regarding the terms sufficient to meet the isometry mapping a weakand n-isometry. Discussion of the concept of isometry on n-normed spaces non-Archimedian, discussed about the concept of weak n-isometry preserves the midpoint and the triangle barycenter 0 1 2 . x x x ? Key words: n-normed spaces, n-normed spacesnon-Archimedian,n- isometry

Kata Kunci : ruang bernorma-n; ruang bernorma-n non-Archimedian; Isometri-n