Advanced Topics of Topology [Working Title]最新文献

Vertex Decomposability of Path Complexes and Stanley’s Conjectures 路径复合体的顶点可分解性与Stanley猜想

Advanced Topics of Topology [Working Title] Pub Date : 2022-02-01 DOI: 10.5772/intechopen.101083

Seyed Mohammad Ajdani, F. Bulnes

{"title":"Vertex Decomposability of Path Complexes and Stanley’s Conjectures","authors":"Seyed Mohammad Ajdani, F. Bulnes","doi":"10.5772/intechopen.101083","DOIUrl":"https://doi.org/10.5772/intechopen.101083","url":null,"abstract":"Monomials are the link between commutative algebra and combinatorics. With a simplicial complex Δ, one can associate two square-free monomial ideals: the Stanley-Reisner ideal IΔ whose generators correspond to the non-face of Δ, or the facet ideal I(Δ) that is a generalization of edge ideals of graphs and whose generators correspond to the facets of Δ. The facet ideal of a simplicial complex was first introduced by Faridi in 2002. Let G be a simple graph. The edge ideal I(G) of a graph G was first considered by R. Villarreal in 1990. He studied algebraic properties of I(G) using a combinatorial language of G. In combinatorial commutative algebra, one can attach a monomial ideal to a combinatorial object. Then, algebraic properties of this ideal are studied using combinatorial properties of combinatorial object. One of interesting problems in combinatorial commutative algebra is the Stanley’s conjectures. The Stanley’s conjectures are studied by many researchers. Let R be a Nn-graded ring and M a Zn-graded R-module. Then, Stanley conjectured that depthM≤sdepthM. He also conjectured that each Cohen-Macaulay simplicial complex is partition-able. In this chapter, we study the relation between vertex decomposability of some simplicial complexes and Stanley’s conjectures.","PeriodicalId":206412,"journal":{"name":"Advanced Topics of Topology [Working Title]","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130270933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

βI-Compactness, βI*-Hyperconnectedness and βI-Separatedness in Ideal Topological Spaces 理想拓扑空间中的βI-紧性、βI*-超连通性和βI-分离性

Advanced Topics of Topology [Working Title] Pub Date : 2022-01-26 DOI: 10.5772/intechopen.101524

Glaisa T. Catalan, Michael P. Baldado Jr, Roberto N. Padua

{"title":"βI-Compactness, βI*-Hyperconnectedness and βI-Separatedness in Ideal Topological Spaces","authors":"Glaisa T. Catalan, Michael P. Baldado Jr, Roberto N. Padua","doi":"10.5772/intechopen.101524","DOIUrl":"https://doi.org/10.5772/intechopen.101524","url":null,"abstract":"Let XτI be an ideal topological space. A subset A of X is said to be β-open if A⊆clintclA, and it is said to be βI-open if there is a set O∈τ with the property 1O−A∈I and 2A−clintclO∈I. The set A is called βI-compact if every cover of A by βI-open sets has a finite sub-cover. The set A is said to be cβI-compact, if every cover Oλ:λ∈Λ of A by β-open sets, Λ has a finite subset Λ0 such that A−∪Oλ:λ∈Λ0∈I. The set A is said to be countably βI-compact if every countable cover of A by βI-open sets has a finite sub-cover. An ideal topological space XτI is said to be βI∗-hyperconnected if X−cl∗A∈I for every non-empty βI-open subset A of X. Two subsets A and B of X is said to be βI-separated if clβIA∩B=∅=A∩clβB. Moreover, A is called a βI-connected set if it can’t be written as a union of two βI-separated subsets. An ideal topological space XτI is called βI-connected space if X is βI-connected. In this article, we give some important properties of βI-open sets, βI-compact spaces, cβI-compact spaces, βI∗-hyperconnected spaces, and βI-connected spaces.","PeriodicalId":206412,"journal":{"name":"Advanced Topics of Topology [Working Title]","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120983145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Clairaut Submersion 克莱罗淹没

Advanced Topics of Topology [Working Title] Pub Date : 2021-12-24 DOI: 10.5772/intechopen.101427

Sanjay Kumar Singh, Punam Gupta

引用次数: 0

The Topology of the Configuration Space of a Mathematical Model for Cycloalkenes 环烯烃数学模型构型空间的拓扑结构

Advanced Topics of Topology [Working Title] Pub Date : 2021-11-11 DOI: 10.5772/intechopen.100723

Y. Kamiyama

引用次数: 0

More Functions Associated with Neutrosophic gsα*- Closed Sets in Neutrosophic Topological Spaces 中性粒细胞拓扑空间中与gsα*-闭集相关的更多函数

Advanced Topics of Topology [Working Title] Pub Date : 2021-09-13 DOI: 10.5772/intechopen.99464

P. Rodrigo, S. Maheswari

引用次数: 1