RT - Journal Article
T1 - Some Results on TVS-cone Normed Spaces and Algebraic Cone Metric Spaces
JF - IJMSI
YR - 2014
JO - IJMSI
VO - 9
IS - 1
UR - http://ijmsi.ir/article-1-360-en.html
SP - 71
EP - 80
K1 - Cone bounded
K1 - Equivalent cone norms
K1 - Algebraically cone metric.
AB - 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.
LA eng
UL http://ijmsi.ir/article-1-360-en.html
M3 10.7508/ijmsi.2014.01.007
ER -