Compact-like abelian groups without non-trivial quasi-convex null sequences

In this paper, we study precompact abelian groups G that contain no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0. We characterize groups with this property in the following classes of groups: (a) bounded precompact abelian groups; (b) minimal abelian groups; (c) totally minimal abelian groups; (d) \omega-bounded abelian groups. We also provide examples of minimal abelian groups with this property, and show that there exists a minimal pseudocompact abelian group with the same property; furthermore, under Martin's Axiom, the group may be chosen to be countably compact minimal abelian.Comment: Final versio

On the Tightness and Long Directed Limits of Free Topological Algebras

For a limit ordinal λ, let (Aα)α \u3c λ be a system of topological algebras (e.g., groups or vector spaces) with bonding maps that are embeddings of topological algebras, and put A = ∪α \u3c λ Aα. Let (A, T) and (A, A) denote the direct limit (colimit) of the system in the category of topological spaces and topological algebras, respectively. One always has T ⊇ A, but the inclusion may be strict; however, if the tightness of A is smaller than the cofinality of λ, then A=T. In 1988, Tkachenko proved that the free topological group F(X) is sequential when Xn is sequential, countably compact, and normal for every n. In particular, F(ω1) is sequential. In this talk, we show that under the same conditions, the free topological vector space V(X) is sequential, and thus countably tight. Consequently, F(ω1) = colimα \u3c ω1 F(α) and V(ω1) = colimα \u3c ω1 V(α) not only as topological algebras, but also as topological spaces

Career Indecision from the Perspective of Time Orientation

The present study focuses on the link between career indecision status and time perspective of high school students. Previous works mainly investigated the relationship between future orientation and career indecision, neglecting attitudes towards other time perspective dimensions, such as the past and the present. Therefore, our aim was to overcome this hiatus by using the Zimbardo Time Perspective Inventory (Zimbardo & Boyd, 1999) and Career Factor Inventory (Chartrand, Robbins, Morrill & Boggs, 1990) in a sample of 683 high school students. By considering variable-centered and person-centered analyses, results suggest that scores on TP factors are closely associated with the career indecision type that one can be classified into. “Path seeker” and “Ready to decide” students have a balanced time perspective; “Chronically indecisive” youngsters have a time perspective pattern which is dominated by the past negative factor and they are less future-oriented; “Choice anxious” students have scores lower on all TP factors (except Past-Negative TP) than any other group

Compactly Supported Homeomorphisms as Long Direct Limits

Let λ be a limit ordinal and consider a directed system of topological groups (Gα)α \u3c λ with topological embeddings as bonding maps and its directed union G=∪α \u3c λGα. There are two natural topologies on G: one that makes G the direct limit (colimit) in the category of topological spaces and one which makes G the direct limit (colimit) in the category of topological groups. For λ = ω it is known that these topologies almost never coincide (Yamasaki\u27s Theorem). In my talk last year, I introduced the Long Direct Limit Conjecture, stating that for λ = ω1 the two topologies always coincide. This year, I will introduce one particular example of such a direct limit: The groups of compactly supported homeomorphisms of the Long Line which is naturally such a directed union of topological groups. I will explain why on this group the two direct limit topologies mentioned above agree (and are equal to the compact open topology). Unfortunately this method only works in dimension one and breaks down as soon as one wants to consider groups of homeomorphisms of the Long Plane or similar two dimensional manifolds

Long colimits of topological groups III: Homeomorphisms of products and coproducts

The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in a number of ways, including as a colimit of homeomorphism groups with a given compact support, or as a subgroup of the homeomorphism group of its Stone-\v{C}ech compactification. A space is said to have the Compactly Supported Homeomorphism Property (CSHP) if these two topologies coincide. The authors provide necessary and sufficient conditions for finite products of ordinals equipped with the order topology to have CSHP. In addition, necessary conditions are presented for finite products and coproducts of spaces to have CSHP

Testing a Possible Way of Geometrization of the Strong Interaction by a Kaluza-Klein Star

Geometrization of the fundamental interactions has been extensively studied during the century. The idea of introducing compactified spatial dimensions originated by Kaluza and Klein. Following their approach, several model were built representing quantum numbers (e.g. charges) as compactified space-time dimensions. Such geometrized theoretical descriptions of the fundamental interactions might lead us to get closer to the unification of the principle theories. Here, we apply a $3+1_C+1$ dimensional theory, which contains one extra compactified spatial dimension $1_C$ in connection with the flavour quantum number in Quantum Chromodynamics. Within our model the size of the $1_C$ dimension is proportional to the inverse mass-difference of the first low-mass baryon states. We used this phenomena to apply in a compact star model -- a natural laboratory for testing the theory of strong interaction and the gravitational theory in parallel. Our aim is to test the modification of the measurable macroscopical parameters of a compact Kaluza-Klein star by varying the size of the compactified extra dimension. Since larger the $R_C$ the smaller the mass difference between the first spokes of the Kaluza-Klein ladder resulting smaller-mass stars. Using the Tolman-Oppenheimer-Volkov equation, we investigate the $M$-$R$ diagram and the dependence of the maximum mass of compact stars. Besides testing the validity of our model we compare our results to the existing observational data of pulsar properties for constraints.Comment: 10 pages, 2 figure