On components of MANR-spaces
On compositions and products of almost continuous functions
On confluently graph-like compacta
For any class 𝒦 of compacta and any compactum X we say that: (a) X is confluently 𝒦-representable if X is homeomorphic to the inverse limit of an inverse sequence of members of 𝒦 with confluent bonding mappings, and (b) X is confluently 𝒦-like provided that X admits, for every ε >0, a confluent ε-mapping onto a member of 𝒦. The symbol 𝕃ℂ stands for the class of all locally connected compacta. It is proved in this paper that for each compactum X and each family 𝒦 of graphs, X is confluently...
On continuity and monotonicity of Darboux functions
On continuous extension of uniformly continuous functions and metrics
We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space (X,d). In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.
On continuous extensions.
On continuous images of almost Tychonoff cubes
On continuous maps in closure spaces.
On continuous surjections from Cantor set.
It is a famous result of Alexandroff and Urysohn that every compact metric space is a continuous image of a Cantor set ∆. In this short note we complement this result by showing that a certain uniqueness property holds. Namely, if (K,d) is a compact metric space and f and g are two continuous mappings from ∆ onto K, the, for every e > 0 there exists a homeomorphism phi of ∆ such that d(g(x), f(phi(x))) < e for all x∆.
On ℳ-contractibility
On contra-precontinuous functions.
On convergence of sequences of functions
On convergence of successive approximations of some generalized contraction mappings
On convergence theory in fuzzy topological spaces and its applications
In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the -relation and the -neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong -compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar...
On Convex Sets with Convex-Hereditary CEP
CEP stands for the compact extension property. We characterize nonlocally convex complete metric linear spaces with convex-hereditary CEP.
On countably paracompact spaces and closed maps
On De Blasi's differentiation theory for multifunctions
On decomposition of fuzzy -continuity.
On decomposition of projections of finite order
On decomposition of spaces on meager sets