Normality in function spaces
Norm-to-weak upper semicontinuous monotone operators are generically strongly continuous.
Note about atom-categories of topological spaces
Note on a Theorem of Kuratowski-Sierpiński
Note on bi-Lipschitz embeddings into normed spaces
Let , be metric spaces and an injective mapping. We put , and (the distortion of the mapping ). We investigate the minimum dimension such that every -point metric space can be embedded into the space with a prescribed distortion . We obtain that this is possible for , where is a suitable absolute constant. This improves a result of Johnson, Lindenstrauss and Schechtman [JLS87] (with a simpler proof). Related results for embeddability into are obtained by a similar method.
Note on connections of the point of continuity property and Kuratowski problem on function having the Baire property
Note on dense covers in the category of locales
In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.
Note on limits of simply continuous and cliquish functions.
Note on quasi-uniform spaces and representable spaces
Note on the selection properties of set-valued semimartingales
Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.
Notes on almost open mappings
Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions
We introduced the notion of -boundedness of a filtered family of operators in the Musielak-Orlicz sequence space of multifunctions. This notion is used to get the convergence theorems for the families of -linear operators, -dist-sublinear operators and -dist-convex operators. Also, we prove that is complete.
Notes on -covers
The main purpose of this paper is to establish general conditions under which -spaces are compact-covering images of metric spaces by using the concept of -covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of -metrizable spaces by compact-covering -maps and -maps.
Notes on quotient maps
Notes on Retracts of Coset Spaces
We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not a retract of...
Nowhere dense sets and real-valued functions with closed graphs.
Nowhere monotone functions and a problem of K.M. Garg
-абсолют и интегрируемые по Риману функции.
O jednom úniku od spojitosti
O бикoмпaктax, лeжaщиx в -пpoизвeдeнияx