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Homological connectivity in random Čech complexes
We study the homology of random Čech complexes generated by a homogeneous Poisson process. We focus on ‘homological connectivity’—the stage where the...
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On the Stone–Čech Compactification Functor and the Normal Extensions of Monoids
AbstractThe paper deals with extensions of algebraic and topological monoids. The extensions are defined by short exact sequences of objects and...
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Properties of Topological Partitions and Map**s of Topological Groups
In this paper, we examine topological partitions of topological spaces that arise in connection with continuous map**s of topological spaces. The...
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Simplicial Chern–Weil theory for coherent analytic sheaves, part II
In the previous part of this diptych, we defined the notion of an admissible simplicial connection , as well as explaining how H.I. Green constructed...
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Relative Čech–Dolbeault homology and applications
We define the relative Dolbeault homology of a complex manifold with currents via a Čech approach, and we prove its equivalence with the relative...
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Residues and Hyperfunctions
We discuss relative Čech-de Rham and relative Čech-Dolbeault cohomologies and their applications. In the de Rham case, we are mainly concerned with...
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Algebraic characterizations of some relative notions of size
We obtain algebraic characterizations of relative notions of size in a discrete semigroup that generalize the usual combinatorial notions of...
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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...
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Local and global coincidence homology classes
For two differentiable maps between two manifolds of possibly different dimensions, the local and global coincidence homology classes are introduced...
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Generic families of finite metric spaces with identical or trivial 1-dimensional persistence
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of...
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Čech Complexes, Čech Homology and Cohomology
Čech complexes are important tools in various fields of Mathematics, in particular in Algebraic Geometry and Commutative Algebra. In Commutative...
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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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Boolean Algebras
The theory of Boolean algebras was founded in 1847 by Boole, who considered it a form of ‘calculus’ adequate for the study of logic. Apart from the...
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An Overview of Deformation Theory of Complex Manifolds
The aim of this chapter is to give a partial and informal introduction to classical deformation theory of complex manifolds and moves around the...