scholarly journals On sequence-covering mssc-images of locally separable metric spaces

2010 ◽  
Vol 87 (101) ◽  
pp. 143-153
Author(s):  
Dung Van
Keyword(s):  
Metric Spaces ◽  
Locally Finite ◽  
Locally Separable Metric Spaces

We characterize sequence-covering (resp., 1-sequence-covering, 2-sequence-covering) mssc-images of locally separable metric spaces by means of ?-locally finite cs-networks (resp., sn-networks, so-networks) consisting of ?0-spaces (resp., sn-second countable spaces, so-second countable spaces). As the applications, we get characterizations of certain sequence-covering, quotient mssc-images of locally separable metric spaces.

scholarly journals On embeddings of locally finite metric spaces into ℓ

2019 ◽  
Vol 474 (1) ◽  
pp. 666-673 ◽  
Author(s):  
Sofiya Ostrovska ◽  
Mikhail I. Ostrovskii
Keyword(s):  
Metric Spaces ◽  
Locally Finite ◽  
Finite Metric Spaces

scholarly journals Sums of finite-dimensional spaces

1969 ◽  
Vol 1 (3) ◽  
pp. 357-361 ◽  
Author(s):  
B.R. Wenner
Keyword(s):  
Metric Spaces ◽  
Dimension Theory ◽  
General Hypothesis ◽  
Locally Finite ◽  
Finite Dimensional ◽  
Locally Countable

Analogues are developed to the sum theorems in the dimension theory of metric spaces. It is shown that, within the class of metric spaces, any locally countable, σ-locally finite, or closure-preserving sum of finite-dimensional sets is countable-dimensional. Similar results are obtained under the more general hypothesis of countable-dimensional rather than finite-dimensional sets.

Weak-open images of locally separable metric spaces

2011 ◽  
Vol 48 (2) ◽  
pp. 145-159
Author(s):  
Zhaowen Li ◽  
Xun Ge ◽  
Qingguo Li
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Weak Base ◽  
Cosmic Space ◽  
Locally Separable Metric Spaces ◽  
Separable Metric Space

In this paper, we prove that a space X is a weak-open compact image of a locally separable metric space if and only if X has a uniform cosmic-weak-base if and only if X is a weak-open compact image of a metric space and a locally cosmic space, and give some internal characterizations of weak-open s-images of locally separable metric spaces.

scholarly journals Further results on images of metric spaces

2015 ◽  
Vol 98 (112) ◽  
pp. 179-191
Author(s):  
Van Dung
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Continuous ◽  
Locally Separable Metric Spaces ◽  
Necessary And Sufficient ◽  
Separable Metric Space

We introduce the notion of an ls-?-Ponomarev-system to give necessary and sufficient conditions for f:(M,M0) ? X to be a strong wc-mapping (wc-mapping, wk-mapping) where M is a locally separable metric space. Then, we systematically get characterizations of weakly continuous strong wc-images (wc-images, wk-images) of locally separable metric spaces by means of certain networks. Also, we give counterexamples to sharpen some results on images of locally separable metric spaces in the literature.

scholarly journals On certain properties characterizing locally separable metric spaces

1967 ◽  
Vol 092 (2) ◽  
pp. 157-161
Author(s):  
Tibor Neubrunn ◽  
Jaroslav Smítal ◽  
Tibor Šalát
Keyword(s):  
Metric Spaces ◽  
Locally Separable Metric Spaces

scholarly journals so-metrizable spaces and images of metric spaces

2021 ◽  
Vol 19 (1) ◽  
pp. 1145-1152
Author(s):  
Songlin Yang ◽  
Xun Ge
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Metrizable Space ◽  
Open Mapping ◽  
Generalized Metric Space ◽  
Locally Finite ◽  
Generalized Metric Spaces ◽  
Covering Mapping ◽  
Generalized Metric ◽  
Metrizable Spaces

Abstract so-metrizable spaces are a class of important generalized metric spaces between metric spaces and s n sn -metrizable spaces where a space is called an so-metrizable space if it has a σ \sigma -locally finite so-network. As the further work that attaches to the celebrated Alexandrov conjecture, it is interesting to characterize so-metrizable spaces by images of metric spaces. This paper gives such characterizations for so-metrizable spaces. More precisely, this paper introduces so-open mappings and uses the “Pomomarev’s method” to prove that a space X X is an so-metrizable space if and only if it is an so-open, compact-covering, σ \sigma -image of a metric space, if and only if it is an so-open, σ \sigma -image of a metric space. In addition, it is shown that so-open mapping is a simplified form of s n sn -open mapping (resp. 2-sequence-covering mapping if the domain is metrizable). Results of this paper give some new characterizations of so-metrizable spaces and establish some equivalent relations among so-open mapping, s n sn -open mapping and 2-sequence-covering mapping, which further enrich and deepen generalized metric space theory.

scholarly journals Uniformization of metric surfaces using isothermal coordinates

2021 ◽  
Vol 47 (1) ◽  
pp. 155-180
Author(s):  
Toni Ikonen
Keyword(s):  
Metric Spaces ◽  
Riemannian Surface ◽  
Locally Finite ◽  
Definition Of ◽  
Isothermal Coordinates ◽  
Geometric Definition ◽  
Euclidean Domains

  We establish a uniformization result for metric surfaces – metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be covered by quasiconformal images of Euclidean domains is quasiconformally equivalent to a Riemannian surface. To prove this, we construct an atlas of suitable isothermal coordinates.

Sign in / Sign up

Export Citation Format

Share Document