In this paper a new class of homeomorphism called minimal Regular weakly and maximal are introduced investigated during process some properties the concepts have been studied.

The homeomorphism problem is, given two compact n-manifolds, is there an algorithm to decide if the manifolds are homeomorphic or not. The homeomorphism problem has been solved for many important classes of 3-manifolds especially those with embedded 2-sided incompressible surfaces (cf [12], [15],[16]), which are called Haken manifolds. It is also well-known that the homeomorphism problem is eas...

We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of Čech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like ti...

We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is a limit of minimally parabolic, geometrically finite Kleinian groups having exactly that homeomorphism type and end invariants. This shows that the Bers-Th...

Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) ≥ 2 and let Γ be a uniform lattice in G. (a) If CH holds, then Γ has a unique asymptotic cone up to homeomorphism. (b) If CH fails, then Γ has 2 ω asymptotic cones up to homeomorphism.

Whittlesey 12,13,14] gave a criterion which decides when two nite 2-dimensional complexes are homeomorphic. We show that graph isomorphism can be reduced eeciently to 2-complex homeomorphism, and that Whittlesey's criterion can be reduced eeciently to graph isomorphism. Therefore graph isomorphism and 2-complex homeomorphism are polynomial-time equivalent.

in this paper, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

We introduce a notion of graph homeomorphisms which uses the concept of dimension and homotopy for graphs. It preserves the dimension of a subbasis, cohomology and Euler characteristic. Connectivity and homotopy look as in classical topology. The Brouwer-Lefshetz fixed point leads to the following discretiszation of the Kakutani fixed point theorem: any graph homeomorphism T with nonzero Lefsch...