Normed Topological Pseudovector Groups

作者：Niemiec Piotr^*

来源：Applied Categorical Structures, 2012, 20(3): 303-322.

DOI：10.1007/s10485-010-9239-7

• Normed vector spaces
• Topological groups
• Locally compact groups
• Valued groups
• Dynamical systems
• Urysohn universal metric space

A normed topological pseudovector group (NTPVG for short) is a valued topological group (V, + ,||center dot||) (not necessarily Abelian) endowed with a continuous scalar multiplication (V, +, parallel to . parallel to), 1 center dot x = x, (st) center dot x = s center dot(t center dot x), t center dot(x + y) = (t center dot x) + (t center dot y) and ||t center dot x|| = t ||x|| for each t, s is an element of R+ and x, y aaEuro parts per thousand V. It is shown that every valued topological group can be isometrically and group-homomorphically embedded in a NTPVG as a closed subset by means of a functor. Locally compact NTPV groups are fully classified. It is shown that the (unbounded) Urysohn universal metric space can be endowed with a structure of a NTPV group of exponent 2.

• 出版日期2012-6