Mathematics – Dynamical Systems
Scientific paper
2011-11-02
Mathematics
Dynamical Systems
Scientific paper
The families of right (left) translation finite subsets of a discrete infinite group $\Gamma$ are defined and shown to be ideals. Their kernels $Z_R$ and $Z_L$ are identified as the closure of the set of products $pq$ ($p\cdot q$) in the \v{C}ech-Stone compactification $\beta\Gamma$. Consequently it is shown that the map $\pi: \beta\Gamma \to \Gamma^{WAP}$, the canonical semigroup homomorphism from $\beta\Gamma$ onto $\Gamma^{WAP}$, the universal semitopological semigroup compactification of $\Gamma$, is a homeomorphism on the complement of $Z_R \cup Z_L$.
No associations
LandOfFree
Translation-finite sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Translation-finite sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Translation-finite sets will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-328312