Some results on dimension theory: Universal spaces
Some theorems on invariance of infinite dimension under open and closed mappings
Spaces with fibered approximation property in dimension n
A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: m × n → M there exists a map g′: m × n → M such that g′ is ɛ-homotopic to g and dim g′ (z × n) ≤ n for all z ∈ m. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij [11] and Tuncali-Valov [10].
Spaces with increment of dimension n
Strong Cohomological Dimension
We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that if X is a separable metric ANR and G is a countable Abelian group. Hence for any separable metric ANR X.
Strongly metrizable spaces of large dimension each separable subspace of which is zero-dimensional
Subspace and addition theorems for extension and cohomological dimensions. A problem of Kuzminov
Suites Fσ -absorbantes en théorie de la dimension
Sul la theorie de la dimension dans les hypergroupes
Sur l’invariance de la dimension infinie forte par t-équivalence
Let X and Y be metric compacta such that there exists a continuous open surjection from onto . We prove that if there exists an integer k such that is strongly infinite-dimensional, then there exists an integer p such that is strongly infinite-dimensional.
The box-counting dimension of the sine-curve
The covering dimension of product of generalized Sorgenfrey lines
The dimension of analytic sets
The dimension of hyperspaces of non-metrizable continua
We prove that, for any Hausdorff continuum X, if dim X ≥ 2 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then either dim C(X) = 2 or C(X) is not a C-space. This generalizes some results known for metric continua.
The dimension of metrizable subspaces of Eberlein compacta and Eberlein compactifications of metrizable spaces
We prove that every Baire subspace Y of c₀(Γ) has a dense metrizable subspace X with dim X ≤ dim Y. We also prove that the Kimura-Morishita Eberlein compactifications of metrizable spaces preserve large inductive dimension. The proofs rely on new and old results concerning the dimension of uniform spaces.
The dimension of products of complete separable metric spaces
The dimension of remainders of rim-compact spaces
Answering a question of Isbell we show that there exists a rim-compact space X such that every compactification Y of X has dim(Y)≥ 1.
The Dimension of the Set of All Finite Subsets of the Continuum
The dimension of X^n where X is a separable metric space
For a separable metric space X, we consider possibilities for the sequence where . In Section 1, a general method for producing examples is given which can be used to realize many of the possible sequences. For example, there is such that , , for n >1, such that , and Z such that S(Z) = 4, 4, 6, 6, 7, 8, 9,.... In Section 2, a subset X of is shown to exist which satisfies and .
The Dimension Print of Most Convex Surfaces.