1,720,996 research outputs found
GROUP ACTION ON RxQ AND FINE GROUP TOPOLOGIES
No full textLet X be a Tikhonov space, H(X) the group of all self-homeomorphisms of X with the usual composition and e:H(X)×X -> X, (f, x) \in f(x), the evaluation map. A group topology on H(X) which makes it a topological group is called admissible if the evaluation map is continuous.
Let LH(X) be the upper semi-lattice of all admissible group topologies on H(X) ordered by the usual inclusion. The author considers the question of when LH(X) has a least element for a non-compact space X. The existence of a least element in LH(X) has been proved for T2 locally compact spaces, T2 rim-compact and locally connected spaces, and so on. Here a spaceX is called rim-compact if every point in X has arbitrarily small neighborhoods with compact boundary. In this paper the author shows that X being rim-compact is not a necessary condition in order for LH(X) to have a least element. It is known that for the set R of real numbers and the set Q
of rational numbers, each with the Euclidean topology, the product R×Q is not rim-compact.Indeed, the author proves that LH(R×Q) has a least element
Topologies on the autohomeomorphic group
No full textAbstracts of the Summer Topology Conference New Yor
Point-Free Geometries: Proximities and Quasi-Metrics
No full textIn the Euclidean geometry points are the primitive entities. Point-based spatial construction is dominant but apparently, in a constructive point of view and a na\"{\i}ve knowledge of space, the region-based spatial theory is more quoted, as recent and past literature strongly suggest. The point-free geometry refers directly to sets, the {\it spatial regions}, and {\it relations between regions} rather than referring to points and sets of points. One of the approach to point-free geometry proposes as primitives the concept of region and quasi-metric, a non-symmetric distance between regions, yielding a natural notion of diameter of a region that, under suitable conditions, allows to reconstruct the canonical model. The intended canonical model is the hyperspace of the non-empty regularly closed subsets of a metric space equipped with the Hausdorff excess. The canonical model can be enriched by adding more qualitative structure involving a distinguished countable subfamily of regions, {\it bounded regions}, and a group of {\it similitudes} preserving bounded regions, so eventually producing a metric geometry whose points, roughly speaking decreasing sequences of bounded regions with vanishing diameters, have some specific features preserved by similitudes and different metric geometries for distinct bounded regions
Point-free geometry with shape
No full textAbstracts of the Summer Tpology Conference On Topology Cape Tow
Special topologies on the autohomeomorphic group of the rational numbers
No full textAbstracts of the Summer Topology Conference Aucklan
Proximity: A powerful tool in function space topologies and hyperspaces
No full textAbstracts Convegno Internazionale di Topologia Generale e Teoria della Forma Perugi
Action, uniformity and proximity Book of Abstracts Seventh Italian-Spanish Conference on general Topology and its Applications
No full textArgomento di una conferenza general
Spazi quasimetrici e topologie ad essi associate
No full textSommario: Si definiscono e si studiano le quasimetriche per un insieme S non vuoto come applicazioni dell' insieme SxS nell'insieme R dei numeri reali soddisfacenti l'assioma della coincidenza e l' assioma triangolare. Si generalizzano , inoltre, risultati di W.A. Wilson [6] e G.E. Albert [1] che si sono interessati delle quasimetriche non negative
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