scholarly journals Order ideal limit points and a generalized Bolzano-theorem

2015 ◽  
pp. 29-37
Author(s):  
Bablu Biswas ◽  
D. K. Ganguly
Keyword(s):  
Order Ideal ◽  
Limit Points ◽  
Ideal Limit

scholarly journals Invariance of ideal limit points

2019 ◽  
Vol 252 ◽  
pp. 169-177 ◽  
Author(s):  
Paolo Leonetti
Keyword(s):  
Limit Points ◽  
Ideal Limit

Investigation of Limit Points and Separation Axioms Using Supra $\beta$-Open Sets

2020 ◽  
Vol 32 (2) ◽  
pp. 171-187
Author(s):  
T. M. Al-Shami ◽  
E. A. Abo-Tabl ◽  
B. A. Asaad
Keyword(s):  
Separation Axioms ◽  
Limit Points

scholarly journals The close relation between border and Pommaret marked bases

2021 ◽  
Author(s):  
Cristina Bertone ◽  
Francesca Cioffi
Keyword(s):  
Finite Order ◽  
Polynomial Ring ◽  
Group Actions ◽  
Close Relation ◽  
Open Covering ◽  
Order Ideal ◽  
Lower Dimension ◽  
Hilbert Schemes ◽  
Affine Spaces ◽  
The Ideal

AbstractGiven a finite order ideal $${\mathcal {O}}$$ O in the polynomial ring $$K[x_1,\ldots , x_n]$$ K [ x 1 , … , x n ] over a field K, let $$\partial {\mathcal {O}}$$ ∂ O be the border of $${\mathcal {O}}$$ O and $${\mathcal {P}}_{\mathcal {O}}$$ P O the Pommaret basis of the ideal generated by the terms outside $${\mathcal {O}}$$ O . In the framework of reduction structures introduced by Ceria, Mora, Roggero in 2019, we investigate relations among $$\partial {\mathcal {O}}$$ ∂ O -marked sets (resp. bases) and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked sets (resp. bases). We prove that a $$\partial {\mathcal {O}}$$ ∂ O -marked set B is a marked basis if and only if the $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked set P contained in B is a marked basis and generates the same ideal as B. Using a functorial description of these marked bases, as a byproduct we obtain that the affine schemes respectively parameterizing $$\partial {\mathcal {O}}$$ ∂ O -marked bases and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked bases are isomorphic. We are able to describe this isomorphism as a projection that can be explicitly constructed without the use of Gröbner elimination techniques. In particular, we obtain a straightforward embedding of border schemes in affine spaces of lower dimension. Furthermore, we observe that Pommaret marked schemes give an open covering of Hilbert schemes parameterizing 0-dimensional schemes without any group actions. Several examples are given throughout the paper.

On the best achievable quality of limit points of augmented Lagrangian schemes

2021 ◽  
Author(s):  
Roberto Andreani ◽  
Gabriel Haeser ◽  
Leonardo M. Mito ◽  
Alberto Ramos ◽  
Leonardo D. Secchin
Keyword(s):  
Augmented Lagrangian ◽  
Limit Points
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