Transitivity and the $\gamma $-space conjecture in ordered spaces

Fuzzy filters in ordered $Gamma$-semirings

We introduce the notion of ideal, prime ideal, lter, fuzzy ideal, fuzzy prime ideal, fuzzy lter of ordered $Gamma$-semiring and study their properties and relations between them. We characterize the prime ideals and lters of ordered $Gamma$-semiring with respect to fuzzy ideals and fuzzy l- ters respectively.

Topology Proceedings 4 (1979) pp. 1-12: QUASI-METRIZABILITY AND THE gamma-SPACE PROPERTY IN CERTAIN GENERALIZED ORDERED SPACES

$L-$ordered Fuzzifying Convergence Spaces

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

Cleavability in Ordered Spaces

In this paper we study the role of cleavability and divisibility in the topology of generalized ordered (GO-)spaces. We characterize cleavability of a GOspace over the class of metrizable spaces, and over the spaces of irrational and rational numbers. We present a series of examples related to characterizations of cleavability over separable metric spaces and over the space of real numbers.

Finite Dimensional Ordered Vector Spaces with Riesz Interpolation and Effros-shen’s Unimodularity Conjecture

It is shown that, for any field F ⊆ R, any ordered vector space structure of F with Riesz interpolation is given by an inductive limit of sequence with finite stages (F,F≥0) (where n does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with F replaced by the integers, Z. Indeed, it shows that although Effros and Shen’s ...