La complétion universelle d'un produit d'espaces complètement réguliers
Large cardinals and Dowker products
We prove that if there is a model of set-theory which contains no first countable, locally compact, scattered, countably paracompact space , whose Tychonoff square is a Dowker space, then there is an inner model which contains a measurable cardinal.
Les espaces topologiques, les espaces de proximité et les espaces uniformes d'un point de vue général
Linear combinations of partitions of unity with restricted supports
Given a locally finite open covering of a normal space X and a Hausdorff topological vector space E, we characterize all continuous functions f: X → E which admit a representation with and a partition of unity subordinate to . As an application, we determine the class of all functions f ∈ C(||) on the underlying space || of a Euclidean complex such that, for each polytope P ∈ , the restriction attains its extrema at vertices of P. Finally, a class of extremal functions on the metric space...
Locally compact perfectly normal spaces may all be paracompact
We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...
Locally nice spaces under Martin's axiom
L-space without any uncountable 0-dimensiolan subspace