-Lindelöf spaces.
Ideal Banach category theorems and functions
Based on some earlier findings on Banach Category Theorem for some “nice” -ideals by J. Kaniewski, D. Rose and myself I introduce the operator ( stands for “heavy points”) to refine and generalize kernel constructions of A. H. Stone. Having obtained in this way a generalized Kuratowski’s decomposition theorem I prove some characterizations of the domains of functions having “many” points of -continuity. Results of this type lead, in the case of the -ideal of meager sets, to important statements...
Ideal equivalences for almost real-compact spaces
Ideals of uniformly continuous mappings on pseudometric spaces
Imbeddings in of m-dimensional compacta with dim(Х×Х)<2m
Imbeddings into and dimension of products
In quest of weaker connected topologies
We study when a topological space has a weaker connected topology. Various sufficient and necessary conditions are given for a space to have a weaker Hausdorff or regular connected topology. It is proved that the property of a space of having a weaker Tychonoff topology is preserved by any of the free topological group functors. Examples are given for non-preservation of this property by “nice” continuous mappings. The requirement that a space have a weaker Tychonoff connected topology is rather...
In search for Lindelöf ’s
It is shown that if is a first-countable countably compact subspace of ordinals then is Lindelöf. This result is used to construct an example of a countably compact space such that the extent of is less than the Lindelöf number of . This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.
Inaccessibility, essential maps, and shape theory
Indicatrix of Banach and a Space of Continuous Functions
Inducing approximations homotopic to maps between inverse limits
Inductive invariants of closed extensions of mappings
Infinite Iterated Function Systems: A Multivalued Approach
We prove that a compact family of bounded condensing multifunctions has bounded condensing set-theoretic union. Compactness is understood in the sense of the Chebyshev uniform semimetric induced by the Hausdorff distance and condensity is taken w.r.t. the Hausdorff measure of noncompactness. As a tool, we present an estimate for the measure of an infinite union. Then we apply our result to infinite iterated function systems.
Initial Morphisms and Monomorphisms.
Injectivity of polyhedra
Inserting measurable functions precisely
A family of subsets of a set is called a -topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A -topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect -topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a -topological version of Katětov-Tong...
Insertion of a Contra-Baire- (Baire-) Function
Necessary and sufficient conditions in terms of lower cut sets are given for the insertion of a Baire- function between two comparable real-valued functions on the topological spaces that -kernel of sets are -sets.
Instability of the eikonal equation and shape from shading
In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. ...
Integral Domain Type Representations in Sheaves and Other Topoi.
Intégrité du complété et théorème de Stone-Weierstrass