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 ...

It has been observed that constructions so apparently different as Kronecker products, extension of the ring of operators of a module, field of quotients of an integral domain, free groups, free topological groups, completion of a uniform space, Cech compactification enter in the same frame. We intend in this paper to explain a rather general process of construction which may be applied to most...

We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

A twistor Cech cohomological characterization of mixed frequency zero rest-mass elds is developed. Using a Cech form of the cup product we derive an expression for the symplectic product of two real mixed frequency scalar elds in terms of a single vertex diagram. An expression for the frequency splitting complex structure of quantum eld theory is derived, and presented by its action on a mixed ...

An n x m rational matrix A is said to be partition regular if for every finite colouring oi \ there is a monochromatic vector x s N with Ax = 0. A set D c f̂J is said to be partition regular for A (or for the system of equations Ax = 0) if for every finite colouring of D there is a monochromatic x e D' with Ax = 6. In this paper we show that for every n there is a set that is partition regular f...

We present two examples of nice normal spaces X having the property that for some xed-point free homeomorphism on X its Cech-Stone extension has a xed point. One of the spaces presented here is locally countable, locally compact, separable , normal, countably paracompact and weakly zero-dimensional. The other one is hereditarily normal and strongly zero-dimensional. Our construction of this exa...