Internal, external boundaries and continuous mappings
Intersection of moving convex sets in a normed space.
Intersections of ANR's
Intersections of essential minimal prime ideals
Let be the set of zero divisor elements of a commutative ring with identity and be the space of minimal prime ideals of with Zariski topology. An ideal of is called strongly dense ideal or briefly -ideal if and is contained in no minimal prime ideal. We denote by , the set of all for which is compact. We show that has property and is compact if and only if has no -ideal. It is proved that is an essential ideal (resp., -ideal) if and only if is an almost locally compact...
Intersections of minimal prime ideals in the rings of continuous functions
A space is called -compact by M. Mandelker if the intersection of all free maximal ideals of coincides with the ring of all functions in with compact support. In this paper we introduce -compact and -compact spaces and we show that a space is -compact if and only if it is both -compact and -compact. We also establish that every space admits a -compactification and a -compactification. Examples and counterexamples are given.
Intuitionistic fuzzy alpha-continuity and intuitionistic fuzzy precontinuity.
Invariance of -spaces under mappings
Invariant two-forms for geodesic flows.
Inverse invariance of metrizability for ordered spaces
Inverse limits of smooth continua
Inverse Sequences and Absolute Co-Extensors
Suppose that K is a CW-complex, X is an inverse sequence of stratifiable spaces, and X = limX. Using the concept of semi-sequence, we provide a necessary and sufficient condition for X to be an absolute co-extensor for K in terms of the inverse sequence X and without recourse to any specific properties of its limit. To say that X is an absolute co-extensor for K is the same as saying that K is an absolute extensor for X, i.e., that each map f:A → K from a closed subset A of X extends to a map F:X...
Inversion-closed space has Daniell property
Investigating the ANR-property of metric spaces
Irreducible images of
Irreducibly confluent mappings
Irresolute multifunctions.
Isometric Embeddings of Pro-Euclidean Spaces
In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank...
Isomorphism of spaces of bounded continuous functions
Isomorphism Problems for the Baire Function Spaces of Topological Spaces
Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first...
Iterated and double limits