REPRESENTASI LINEAR KONTINU DARI GRUP TOPOLOGIS KE DALAM RUANG VEKTOR TOPOLOGIS CONTINUOUS LINEAR REPRESENTATIONS FROM TOPOLOGICAL GROUPS INTO TOPOLOGICAL VECTOR SPACES

Palupi, Diah Junia Eksi, Setyadji

2015 | Tesis | FMIPA

This dissertation research has been done to have a representation from a topological group into a topological vector space. Each non empty set can always be a topological space, such that groups and vector spaces can be a topological space. Through a continuous mapping on a Cartesian product of topological spaces, in particular the topological space of a group and a vector space. We have a topological group and a topological vector space. A liinear representation is a homomorphism of a group into a set of linear operators on a vector space into itself, which satisfies some axioms. By using concepts of topology, a topological group, and the topological vector space, we observe a continuous linear representation of topological groups into a topological vector space. Futhermore, we have some special continuous linear representations, that are called a bar continuous linear representation, a subrepresentation, a quotient representation and the relationship of them. We have some properties of a continuous linear representation as irredusible, complete redusible, such that every irredusible continuous linear representation is complete redusible and if given a complete reducible continuous linear representation, we obtain a decomposition of the representation space, that is a decomposition of a topological vector space.

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