For Tychonoff X and α an infinite cardinal, let αdef X := the minimum number of α cozero-sets of the Čech-Stone compactification which intersect to X (generalizing R-defect), and let rtX := minα max(α, α def X). Give C(X) the compact-open topology. It is shown that τC(X) ≤ nχC(X) ≤ rtX = max(L(X), L(X) def X), where: τ is tightness; nχ is the network character; L(X) is the Lindelöf number. For ...

Applied to a continuous surjection π : E → B of completely regular Hausdorff spaces E and B, the Stone-Čech compactification functor β yields a surjection βπ : βE → βB. For an n-fold covering map π, we show that the fibres of βπ, while never containing more than n points, may degenerate to sets of cardinality properly dividing n. In the special case of the universal bundle π : EG → BG of a p-gr...

The Stone-Čech compactification of the natural numbers βω (or equivalently, the space of ultrafilters on the subsets of ω) is a well-studied space with interesting properties. Replacing the subsets of ω by partitions of ω in the construction of the ultrafilter space gives non-homeomorphic spaces of partition ultrafilters corresponding to βω. We develop a general framework for spaces of this typ...

We present sufficient conditions for the cohomology of a closed aspherical manifold to be proper Lipschitz in sense of Connes-Gromov-Moscovici [CGM]. The conditions are stated in terms of the Stone-Čech compactification of the universal cover of a manifold. We show that these conditions are formally weaker than the sufficient conditions for the Novikov conjecture given in [CP]. Also we show tha...

We describe the semilattice of ordered compactifications ofX×Y smaller than βoX×βoY whereX and Y are certain totally ordered topological spaces, and where βoZ denotes the Stone–Čech orderedor Nachbin-compactification of Z. These basic cases are used to illustrate techniques for describing the semilattice of ordered compactifications ofX×Y smaller than βoX×βoY for arbitrary totally ordered topol...

We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological ...

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions extensions of this theorem. All these theorems deal with central sets, its origin from the algebra Stone–Čech compactification arbitrary semigroup, say βS. It can be proved that every closed subsemigroup βS is generated a filter. We will show that, under some restr...

In this paper, new methods for analyzing models of weak subsystems Peano Arithmetic are proposed. The focus will be on the study algebro-combinatoric properties certain definable cuts. Their relationship with segments that satisfy more induction, those limited by standard powers/roots an element, and also sets in Bounded Induction is studied. As a consequence, some considerations Π 1 -interpret...