Ideals of uniformly continuous mappings on pseudometric spaces
If it looks and smells like the reals...
Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if is homeomorphic to ℝ, then . The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.
Images of arcs - a nonseparable version of the Hahn-Mazurkiewicz theorem
Imbedding locally convex lattices into compact lattices
Imbeddings in of m-dimensional compacta with dim(Х×Х)<2m
Imbeddings into and dimension of products
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
Indecomposable continua and the fixed point property II
Indecomposable continua with one and two composants
Independence in Klein spaces
Induced almost continuous functions on hyperspaces
For a metric continuum X, let C(X) (resp., ) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and be the induced functions given by and . In this paper, we prove that: • If is almost continuous, then f is continuous. • If C(f) is almost continuous and X is locally connected, then f is continuous. • If X is not locally connected, then there exists an almost continuous function f: X → [0,1] such that...
Inductive čech completeness and dimension
Inductive dimensions for completely regular spaces
Inductive dimensions modulo simplicial complexes and ANR-compacta
We introduce and investigate inductive dimensions 𝒦 -Ind and ℒ-Ind for classes 𝒦 of finite simplicial complexes and classes ℒ of ANR-compacta (if 𝒦 consists of the 0-sphere only, then the 𝒦 -Ind dimension is identical with the classical large inductive dimension Ind). We compare K-Ind to K-Ind introduced by the author [Mat. Vesnik 61 (2009)]. In particular, for every complex K such that K * K is non-contractible, we construct a compact Hausdorff space X with K-Ind X not equal to K-dim X.
Inductive dimensions of the inverse limit spaces
Inductive invariants of closed extensions of mappings
Inessentiality with respect to subspaces
Let X be a compactum and let be a countable family of pairs of disjoint subsets of X. Then A is said to be essential on Y ⊂ X if for every closed separating and the intersection is not empty. So A is inessential on Y if there exist closed separating and such that does not intersect Y. Properties of inessentiality are studied and applied to prove: Theorem. For every countable family of pairs of disjoint open subsets of a compactum X there exists an open set G ∩ X on which A is...
Infinite games and chain conditions
We apply the theory of infinite two-person games to two well-known problems in topology: Suslin’s Problem and Arhangel’skii’s problem on the weak Lindelöf number of the topology on a compact space. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable, and 2) in every compact space satisfying the game-theoretic version of the weak Lindelöf...
Infinite uniform dimension