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Mapping theorems on countable tightness and a question of F. Siwiec

Shou Lin, Jinhuang Zhang (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper s s -quotient maps and s s q -spaces are introduced. It is shown that (1) countable tightness is characterized by s s -quotient maps and quotient maps; (2) a space has countable tightness if and only if it is a countably bi-quotient image of a locally countable space, which gives an answer for a question posed by F. Siwiec in 1975; (3) s s q -spaces are characterized as the s s -quotient images of metric spaces; (4) assuming 2 ω < 2 ω 1 , a compact T 2 -space is an s s q -space if and only if every countably compact subset...

Maps with dimensionally restricted fibers

Vesko Valov (2011)

Colloquium Mathematicae

We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber f - 1 ( y ) belongs to a class S of spaces, then there exists an F σ -set A ⊂ X such that A ∈ S and d i m f - 1 ( y ) ∖ A = 0 for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all g ∈ C ( X , n + 1 ) .

Metric enrichment, finite generation, and the path coreflection

Alexandru Chirvasitu (2024)

Archivum Mathematicum

We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally ℵ 1 -presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry- ℵ 0 -generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results include...

Minimal bi-Lipschitz embedding dimension of ultrametric spaces

Jouni Luukkainen, Hossein Movahedi-Lankarani (1994)

Fundamenta Mathematicae

We prove that an ultrametric space can be bi-Lipschitz embedded in ℝ n if its metric dimension in Assouad’s sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.

Notes on c f p -covers

Shou Lin, Peng Fei Yan (2003)

Commentationes Mathematicae Universitatis Carolinae

The main purpose of this paper is to establish general conditions under which T 2 -spaces are compact-covering images of metric spaces by using the concept of c f p -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 g -metrizable spaces by compact-covering σ -maps and m s s c -maps.

On an affirmative answer to Y. Tanaka's and Y. Ge's problem

Luong Quoc Tuyen (2017)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we give an affirmative answer to the problem posed by Y. Tanaka and Y. Ge (2006) in "Around quotient compact images of metric spaces, and symmetric spaces", Houston J. Math. 32 (2006) no. 1, 99-117.

Currently displaying 101 – 120 of 198