Caractérisation d'espaces polonais d'après des travaux récents de J. P. R. Christensen et D. Preiss
Cardinalities of metric completions
Cauchy nets and open colorings.
Cauchy Sequences in Quasi-Pseudo-Metric Spaces.
Central subsets of Urysohn universal spaces
A subset of a metric space is central iff for every Katětov map upper bounded by the diameter of and any finite subset of there is such that for each . Central subsets of the Urysohn universal space (see introduction) are studied. It is proved that a metric space is isometrically embeddable into as a central set iff has the collinearity property. The Katětov maps of the real line are characterized.
Characterizations of absolute -sets
Characterizations of metric completeness
Closed, continuous images of complete metric spaces
Cofinal completeness of the Hausdorff metric topology
A net in a Hausdorff uniform space is called cofinally Cauchy if for each entourage, there exists a cofinal (rather than residual) set of indices whose corresponding terms are pairwise within the entourage. In a metric space equipped with the associated metric uniformity, if each cofinally Cauchy sequence has a cluster point, then so does each cofinally Cauchy net, and the space is called cofinally complete. Here we give necessary and sufficient conditions for the nonempty closed subsets of the...
Common fixed point theorem of Altman integral type mappings.
Common Fixed Point Theorems in a Complete 2-metric Space
In the present paper, we establish a common fixed point theorem for four self-mappings of a complete 2-metric space using the weak commutativity condition and -contraction type condition and then extend the theorem for a class of mappings.
Commuting contractive families
A family f₁,..., fₙ of operators on a complete metric space X is called contractive if there exists a positive λ < 1 such that for any x,y in X we have for some i. Austin conjectured that any commuting contractive family of operators has a common fixed point, and he proved this for the case of two operators. We show that Austin’s conjecture is true for three operators, provided that λ is sufficiently small.
Completeness and Fixed-Points.
Computing complexity distances between algorithms
We introduce a new (extended) quasi-metric on the so-called dual p-complexity space, which is suitable to give a quantitative measure of the improvement in complexity obtained when a complexity function is replaced by a more efficient complexity function on all inputs, and show that this distance function has the advantage of possessing rich topological and quasi-metric properties. In particular, its induced topology is Hausdorff and completely regular. Our approach is applied to the measurement...
Concerning locally homotopy negligible sets and characterization of -manifolds
Connected economically metrizable spaces
A topological space is non-separably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a non-separably connected complete metric space X under a monotone quotient map. The metric of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set does not exceed the density of A, . The construction of the space X determines a functor : Top...
Constructive irrational space.
Contractions of Nadler type on partial tvs-cone metric spaces
This paper introduces partial tvs-cone metric spaces as a common generalization of both tvs-cone metric spaces and partial metric spaces, and gives a new fixed point theorem for contractions of Nadler type on partial tvs-cone metric spaces. As corollaries, we obtain the main results of S. B. Nadler (1969), D. Wardowski (2011), S. Radenović et al. (2011) and H. Aydi et al. (2012) are deduced.
Convergence results for a class of abstract continuous descent methods.
Convergences for the group of real numbers