KESAMAAN TOPOLOGI DI RUANG BERNORMA DAN RUANG BERNORMA-G

JULITA SARI, NIM. 17106010033 (2021) KESAMAAN TOPOLOGI DI RUANG BERNORMA DAN RUANG BERNORMA-G. Skripsi thesis, FAKULTAS SAINS DAN TEKNOLOGI.

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Abstract

G-normed space was first introduced by Kamran Alam Khan (2014). A G-normed space is a vector space equipped with a G-norm function fulfilling five axioms. G-normed space is a special case of normed linear space with the definition of a certain norm function, so that every concept, meaning and characteristics that apply in normalized space also applies to G-normed space. Previous researchers mentioned that the G-normed space is an generalization of the normed linear space. However, this study shows that the topology in G-normed space is the same as the topology in normed linear space. The process of constructing topological similarities is carried out by showing that the basis for the topology in G-normed space is the same as the basis for the topology in normed linear space. This results in the topology in G-normed space same as the topology in normed linear space. Therefore the G-normed space is not an generalization of the normed linear space.

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