We provide examples of homogeneous spaces which are neither symmetric spaces nor real cohomology spheres, yet have the property that every invariant metric is geometrically formal. We also extend the known obstructions to geometric formality to some new classes of homogeneous spaces and of biquotients, and to certain sphere bundles.

Dynamical algebraic structures, pointfree topological spaces and Hilbert’s program A possible relevant meaning of Hilbert’s program is the following one : “give a constructive semantic for classical mathematics”. More precisely, give a systematic interpretation of classical abstract proofs (that use Third Excluded Middle and Choice) about abstract objects, as constructive proofs about construct...

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieck’s view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers an...

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieck’s view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers an...

The problem of Proximity Searching in Metric Spaces consists in finding the elements of a set which are close to a given query under some similarity criterion. In this paper we present a new methodology to solve this problem, which uses a t-spanner G′(V,E) as the representation of the metric database. A t-spanner is a subgraph G′(V,E) of a graph G(V,A), such that E ⊆ A and G′ approximates the s...

In summability theory, de la Vallée-Poussin’s mean is first used to define the (V, λ)-summability by Leindler [9]. Malkowsky and Savaş [14] introduced and studied some sequence spaces which arise from the notion of generalized de la ValléePoussin mean. Also the (V, λ)-summable sequence spaces have been studied by many authors including [6] and [20]. Recently, there has been a lot of interest in...