In this paper, we prove that when a n-D cubical set is continuously well-composed (CWC), is, the boundary of its continuous analog topological $$(n-1)$$ -manifold, then it digitally (DWC), which means does not contain any critical configuration. We result thanks to local homology. This paper sequel previous where proved DWCness imply CWCness in 4D.

where D is some small category, F is a functor from D to the category of spaces, and, for each object d of D, F (d) has the homotopy type of BH for some subgroup H of G. An expression like 1.1 is sometimes called a homology approximation to BG or a homology decomposition of BG, and can be used either to make calculations with BG or to prove general theorems about BG by induction. (Of course an ...

The Barvinok rank of a d × n matrix is the minimum number of points in R such that the tropical convex hull of the points contains all columns of the matrix. The concept originated in work by Barvinok and others on the travelling salesman problem. Our object of study is the space of real d × n matrices of Barvinok rank two. Let Bd,n denote this space modulo rescaling and translation. We show th...

In the paper we describe complexes whose homologies are naturally isomorphic to the first term of the Vassiliev spectral sequence computing (co)homology of the spaces of long knots in R, d ≥ 3. The first term of the Vassiliev spectral sequence is concentrated in some angle of the second quadrant. In homological case the lower line is the bialgebra of chord diagrams (or its superanalog if d is e...

We consider complexes (X , d) of nuclear Fréchet spaces and continuous boundary maps dn with closed ranges and prove that, up to topological isomorphism, (Hn(X , d)) ∗ ∼= H(X ∗, d∗), where (Hn(X , d)) ∗ is the strong dual space of the homology group of (X , d) and H(X ∗, d∗) is the cohomology group of the strong dual complex (X ∗, d∗). We use this result to establish the existence of topologica...

background: colibacillosis, caused by different serotypes of avian pathogenic escherichia coli (apec), is one of the important diseases in poultry industry. the isolate o78 is the most prevalent serotype of apec in iran. one of the apec virulence factors, increased serum survival (iss) gene, is related to serum resistance. the usual form of colibacillosis in avian is extraintestinal, and serum ...

background: no data is available on morphology and genetic characteristics of echinococcus granulosus derived from donkeys of iran, despite of its existence in donkeys.in the present study morphometric variations of the rostellar hooks of protoscoleces and genotype characteristics of hydatid cyst of donkey from iran were determined. methods: protoscoleces prepared from hydatid cyst of donkey of...

In Mathematical Morphology (MM), dynamics are used to compute markers proceed for example watershed-based image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) represents stability of extrema function. Since these concepts similar on functions, we studied their relationship found, proved, that they equal 1D functions. Here, pr...