In this paper, we introduce and explore γ-S-closed spaces. It is evident by definition that γ-S-closed space coincides with γ-s-closed space, if the underlying space is γ-extremally-disconnected. AMS (MOS) Subject Classification Codes: 54A05, 54A10, 54D10, 54D99.

We use algorithms developed recently for the study of linear groups to investigate a sequence of matrix groups defined over GF(2); these are images of representations of certain finitely presented groups considered by Soicher in a study of simplicial complexes related to the Suzuki sequence graphs.

A variety of questions in combinatorics lead one to the task of analyzing the topology of a simplicial complex, or a more general cell complex. However, there are few general techniques to aid in this investigation. On the other hand, the subjects of differential topology and geometry are devoted to precisely this sort of problem, except that the topological spaces in question are smooth manifo...

We shall explain some of the results and questions in a beautiful 1978 paper [3] by Daniel Quillen. He relates properties of groups to homotopy properties of the simplicial complexes of certain posets constructed from the group. He does not explicitly think of these posets as finite topological spaces. He seems to have been unaware of the earlier papers of McCord [2] and Stong [4] that we have ...

In this paper we study a system of nonlinear elliptic equations, known as thèvortex equations' in 2 dimensions, arising from the eld-theoretical descriptions of several models in physics. When the underlying space is a closed surface, we prove the existence and uniqueness of a solution under a necessary and suucient condition. When the space is R 2 , we establish the existence, uniqueness and s...

The first representation theorem establishes a correspondence between positive, self-adjoint operators and closed, positive forms on Hilbert spaces. The aim of this paper is to show that some of the results remain true if the underlying space is a reflexive Banach space. In particular, the construction of the Friedrichs extension and the form sum of positive operators can be carried over to thi...

Given any finite simplicial complex ∆, we show how to construct from a colouring χ of ∆ a new simplicial complex ∆χ that is balanced and vertex decomposable. In addition, the h-vector of ∆χ is precisely the f -vector of ∆. Our construction generalizes the “whiskering” construction of Villarreal, and Cook and Nagel. We also reverse this construction to prove a special case of a conjecture of Coo...