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Topological structure of the space of composition operators on \(L^{\!\infty }\) of an unbounded, locally finite metric space
We study properties of the topological space of composition operators on the Banach algebra of bounded functions on an unbounded, locally finite...
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Locally finite ultrametric spaces and labeled trees
It is shown that a locally finite ultrametric space ( X , d ) is generated by a labeled tree if and only if for every open ball B ⊆ X there is a point c ...
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Topological aspects of the space of metric measure spaces
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces...
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The Lipschitz-Free Space Over a Length Space is Locally Almost Square but Never Almost Square
We prove that the Lipschitz-free space over a metric space M is locally almost square whenever M is a length space. Consequently, the Lipschitz-free...
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On minimal immersions of a singular non-CSC extremal Kähler metric into 3-dimensional space forms
On any compact Riemann surface there always exists a singular non-CSC (constant scalar curvature) extremal Kähler metric which is called a non-CSC...
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The metric completion of the space of vector-valued one-forms
The space of full-ranked one-forms on a smooth, orientable, compact manifold (possibly with boundary) is metrically incomplete with respect to the...
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On the additivity of strong homology for locally compact separable metric spaces
We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of...
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Locally Compact Quantum Metric Spaces and Spectral Triples
In this chapter, we start by giving an overview of quantum (locally) compact metric spaces. Then, we show that we can associate quantum compact...
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Locally Convex Spaces
This chapter starts recalling the definitions of Hausdorff topological space, metric space, and normed space. Examples of Banach sequence spaces, of...
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Uniformity and Loewner Condtions of Metric Spaces
In this paper, we establish four equivalent conditions in the metric space setting. These conditions concern the (inner) uniformity of metric spaces,...
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Local rigidity of the Teichmüller space with the Thurston metric
We show that every ℝ-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by...
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The Covariance Metric in the Blaschke Locus
We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichmüller space and study its Riemannian...
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Balayage of measures on a locally compact space
We develop a theory of inner balayage of a positive Radon measure μ of finite energy on a locally compact space X to arbitrary A ⊂ X , thereby...
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Metric Characterizations of Projective-Metric Spaces
This chapter is concerned with the study of projective-metric spaces, that is, metrics on open subsets of projective space whose geodesics are the...
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Homeomorphisms of Finite Metric Distortion Between Riemannian Manifolds
The theory of multidimensional quasiconformal map**s employs three main approaches: analytic, geometric (modulus) and metric ones. In this paper,...
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Compact and Locally Compact Spaces
The concept of compactness of a set is pervasive in analysis. This chapter is devoted to the study of compact spaces and locally compact spaces. The...