To View The Abstract, Please Click On PDF File.

Let S be a semitopological semigroup. The wap- compact-ification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the Lmc- COMPACTIFICATION of semigroup S is a universal semigroup COMPACTIFICATION of S, which are denoted by Swap and SLmc respectively. In this paper, an internal construction of the wap-COMPACTIFICATION of a semitopological semigroup is constructed as a space of z-filters. Also we obtain the cardinality of Swap and show that if Swap is the one point COMPACTIFICATION then (SLmc - S) * SLmc is dense in SLmc - S.

Let X be a zero-dimensional space and Cc(X) denote the functionally countable subalgebra of C(X). It is well known that , 0X (the Banaschewski compactfication of X) is a quotient space of , X. In this article, we investigate a construction of , 0X via , X by using Cc(X) which determines the quotient space of , X homeomorphic to , 0X. Moreover, the construction of , 0X via , CcX (the subspace {p 2 , X: 8f 2 Cc(X), f, (p) < 1} of , X) is also investigated.

In this paper by combining the concepts of ultrafilters and multiplicative means in a nice way we find a good tool for dealing with the Stone -Č ech COMPACTIFICATION of infinite discrete semigroups.

Please click on PDF to view the abstract

In this paper, we characterize the function space and L1-space of the [topological] tensor product of [topological] semigroups. As a consequence, for arbitrary [topological] groups G1 and G2, it will be shown that G1×G2 is an extension of G1ÄsG2  by a proper normal subgroup N i,e G1ÄsG2=G1×G2/N

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 group are obtained

The Wallman basis of a frame and the corresponding induced COMPACTIFICATION was first investigated by Baboolal [2]. In this paper, we provide an intrinsic characterisation of S-metrizability in terms of the Wallman basis of a frame. Particularly, we show that a connected, locally connected frame is S-metrizable if and only if it has a countable locally connected and uniformly connected Wallman basis.

In this paper, the concept of soft ultra lters is introduced and some of the related structures such as soft Stone- Cech compacti cation, principal soft ultra lters and basis for its topology are studied.