Common fixed point Theorems for non compatible mappings in fuzzy metric spaces.
Compactly generated shape theories
Compactness in Metric Spaces
In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness,...
Complete function spaces.
Completeness and Fixed-Points.
Concerning certain minimal cover refineable spaces
Condiciones suficientes para la paracompacidad-c. Aplicación a un teorema de metrización.
Congruent Embedding of Metric Quadruples on a Unit Sphere.
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...
Connectedness of complete metric groups
Constant and variable drop theorems on metrizable locally convex spaces
Constant Distortion Embeddings of Symmetric Diversities
Diversities are like metric spaces, except that every finite subset, instead of just every pair of points, is assigned a value. Just as there is a theory of minimal distortion embeddings of fiite metric spaces into L1, there is a similar, yet undeveloped, theory for embedding finite diversities into the diversity analogue of L1 spaces. In the metric case, it iswell known that an n-point metric space can be embedded into L1 withO(log n) distortion. For diversities, the optimal distortion is unknown....
Contractive fixed points
Convergence in compacta and linear Lindelöfness
Let be a compact Hausdorff space with a point such that is linearly Lindelöf. Is then first countable at ? What if this is true for every in ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when is, in addition, -monolithic. We also prove that if is compact, Hausdorff, and is strongly discretely Lindelöf, for every in , then is first countable. An example of linearly Lindelöf...
Correction to the paper: A new look at pointfree metrization theorems
Correction to the paper: On linear functorial operators extending pseudometrics
Correction to the paper: Pairwise monotonically normal spaces
Corrections to my paper "Investigating the ANR-property of metric spaces" (Fund. Math. 124 (1984), 243-254)
Countable Compact Scattered T₂ Spaces and Weak Forms of AC
We show that: (1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T₂ topological space is zero-dimensional. (2) If every countable union of countable sets of reals is countable, then a countable compact T₂ space is scattered iff it is metrizable. (3) If the real line ℝ can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional T₂ space...
Countable sums and products of Loeb and selective metric spaces
We investigate the role that weak forms of the axiom of choice play in countable Tychonoff products, as well as countable disjoint unions, of Loeb and selective metric spaces.