In this short note we provide an example of a semi-linear group G which does not admit a semi-linear affine embedding; in other words, there is no semi-linear isomorphism between topological groups f : G → G′ ⊆ Mm, such that the group topology on G′ coincides with the subspace topology induced by Mm. Let M be an o-minimal structure. By “definable” we mean “definable in M” possibly with paramete...

Gaye Williams and David Clarke University of Melbourne, Melbourne, Australia g [email protected] [email protected] 2 This paper addresses issues related to the triangulation of data in classroom video research—in particular the contribution of the student voice to the research methodology. The case of a Year 8 boy—Leon—is used to illustrate the multiple interpretations that m...

We revisit the parameterized model checking problem for token-passing systems and specifications in indexed CTL∗\X. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed CTL∗\X in uni-directional token rings can be reduced to checking rings up to some cutoff size. Clarke et al. (2004) have shown a similar result for general topologies and indexed LTL\X, provi...

The concept of an M-approximative system is introduced. Basic properties of the category of M-approximative systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximative systems. Keywords— Approximative operator...

Given a group (G, ·), G ⊆M, definable in a first order structureM = (M, . . .) equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V ⊆ G and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from M. Likewise we topologize tra...

Let $R$ be a $G$-graded ring and M $R$-module. We define the graded primary spectrum of $M$, denoted by $\mathcal{PS}_G(M)$, to set all submodules $Q$ such that $(Gr_M(Q):_R M)=Gr((Q:_R M))$. In this paper, we topology on $\mathcal{PS}_G(M)$ having Zariski prime $Spec_G(M)$ as subspace topology, investigate several topological properties space.