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One of the main problems in utility theory is to find conditions which imply the numerical representability of topological spaces on which a preorder, or partial order, is defined. This study has reached a wide development in the literature: see, for instance, the works of Eilenberg, Debreu, Fleischer and Jaffray on completely preordered topological spaces [9, 7, 10, 15], and the seminal book b...

The main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (briefly soft rgb-closed set) Moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g$alpha$-closed, soft g$alpha$b-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and w...

The fuzzy concept has invaded all branches of Mathematics ever since the introduction of fuzzy set by Zadeh [10]. Fuzzy sets have applications in many fields such as information [5] and control [8]. The theory of fuzzy topological spaces was introduced and developed by Chang [3] and since then various notions in classical topology have been extended to fuzzy topological spaces. Sostak [6] intro...

The majority of gastrointestinal (GI) foreign bodies (FBs) discovered in adults are the result of intentional ingestion, most of which are found in patients with a preexisting psychiatric illness, with substance abuse disorders, or in people seeking secondary gain. No similar case of internal injuries following unintentional ingestion of a barbecue grill cleaning brush bristle has been reported...

1.1. Principal G-bundles. Topology is concerned with topological spaces and continuous maps between them. But the data is a topological space of so complicated and infinite in nature that it can be very difficult even to tell when two topological spaces are “the same.” For instance, all n-dimensional manifolds look locally the same. A central theme in algebraic topology is to attach algebraic i...

Two approaches to equivariant homotopy theory in a topological or ordinary Quillen model category are studied and compared. For the topological model category of spaces, we recover that the categories of topological presheaves indexed by the orbit category of a fixed topological group G and the category of G-spaces form Quillen equivalent model categories.

I would like to thank the organizers of the UNISA Topology Workshop, Koena Rufus Nailana and Sergio Salbany, for doing an excellent job acquiring funding, making arrangements, and especially for assembling an enthusiastic group of participants. An ordered topological space (X, τ,≤) is a set X with a topology τ and a partial order ≤. We usually assume some forms of compatibility between the topo...

What parts of classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T0 or T1, but not T2 (i.e. not Hausdorff)? This question has been addressed by Victor Selivanov in a series of papers centered on algebraic domains. And recently it has been considered by Matthew de Brecht for quasi-Polish spaces, a framework that contains both countably...

In this paper we present new forms of the classical separation axioms on topological spaces. Our constructions generate a method to refine separation properties when passing to the quotient space and our results may be useful in the study of algebraic topological structures, such as topological groups and topological vector spaces. AMS subject classification: 54D10, 54D15, 54H11, 54H13.