Compact-like properties in hyperspaces
Compactness and convergence of set-valued measures
We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.
Compactness as -pseudocompactness
Compactness in the First Baire Class and Baire-1 Operators
For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M,...
Compactness of trajectories of dynamical systems in complete uniform spaces
Comparing measure theoretic entropy for -finite measures with topological entropy
Complements of solenoids in are m-spaces
Complete function spaces.
Complete rings of functions and Wallman-Frink compactifications
Completely continuous functions in intuitionistic fuzzy topological spaces
In this paper, after giving the basic results related to the product of functions and the graph of functions in intuitionistic fuzzy topological spaces, we introduce and study the concept of fuzzy completely continuous functions between intuitionistic fuzzy topological spaces.
Completely continuous images of nearly paracomact spaces
Completely -continuous multifunctions.
Completely regular modification and products
Completely regular spaces
We conduct an investigation of the relationships which exist between various generalizations of complete regularity in the setting of merotopic spaces, with particular attention to filter spaces such as Cauchy spaces and convergence spaces. Our primary contribution consists in the presentation of several counterexamples establishing the divergence of various such generalizations of complete regularity. We give examples of: (1) a contigual zero space which is not weakly regular and is not a Cauchy...
Completeness properties of function rings in pointfree topology
This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or -complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.
Completion as reflection
Completion theorem for uniform entropy
Modifying Bowen's entropy, we introduce a new uniform entropy. We prove that the completion theorem for uniform entropy holds in the class of all metric spaces. However, the completion theorem for Bowen's entropy does not hold in the class of all totally bounded metric spaces.
Complexity of the class of Peano functions
We evaluate the descriptive set theoretic complexity of the space of continuous surjections from to .
Component restriction property for classes of mappings.
Composition of functions.