Continuously Representable Topological Groups with Indecomposable Representations of Bounded Degree

Key Points

• The aim is to explore conditions under which a topological group can be represented through indecomposable representations.
• Establish a framework for topological groups and their representations.
• Analyze families of continuous indecomposable representations in finite-dimensional spaces.
• Examine the implications of representations of bounded degree.
• A topological group with the specified representation properties separates its elements.
• It is proven that such groups are finite extensions of commutative groups with plenty of continuous characters.