For every finitely generated free group $F$, we construct an irreducible open $3$-manifold $M_F$ whose end set is homeomorphic to a Cantor set, and with the homogeneity of isomorphic $F$. The all self-homeomorphisms that extend homeomorphisms entire $3$-manifold. This extends earlier result constructs, for each abelian $G$, $M_G$ $G$. method used in proof our main also shows if $G$ Cayley graph...

In digital geometry, objects such as digital straight lines can be considered as equivalent classes of Euclidean straight lines with respect to a digitization process. This paper investigates the analysis of the set of straight lines whose digitization is a given digital straight segment with the help of tools from integral geometry. After a definition of a measure on such sets, we illustrate s...