TY - JOUR
T1 - Some Results on TVS-cone Normed Spaces and Algebraic Cone Metric Spaces
TT - نتایجی روی فضاهای نرمدار مخروطی
JF - IJMSI
JO - IJMSI
VL - 9
IS - 1
UR - http://ijmsi.ir/article-1-360-en.html
Y1 - 2014
SP - 71
EP - 80
KW - Cone bounded
KW - Equivalent cone norms
KW - Algebraically cone metric.
N2 - In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we introduce the notion of algebraically cone metric and we will show that every algebraically cone metric space has a topology.
M3 10.7508/ijmsi.2014.01.007
ER -