Topic
Interior
About: Interior is a research topic. Over the lifetime, 136 publications have been published within this topic receiving 2118 citations.
Papers published on a yearly basis
Papers
TL;DR: It is shown that a soft topological space gives a parametrized family of topological spaces and it is established that the converse does not hold.
Abstract: In the present paper we introduce soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of soft open sets, soft closed sets, soft closure, soft interior points, soft neighborhood of a point and soft separation axioms are introduced and their basic properties are investigated. It is shown that a soft topological space gives a parametrized family of topological spaces. Furthermore, with the help of an example it is established that the converse does not hold. The soft subspaces of a soft topological space are defined and inherent concepts as well as the characterization of soft open and soft closed sets in soft subspaces are investigated. Finally, soft T"i-spaces and notions of soft normal and soft regular spaces are discussed in detail. A sufficient condition for a soft topological space to be a soft T"1-space is also presented.
1,080 citations
TL;DR: In this article, the number of equivalence classes under integer unimodular transformations of lattice poly topes of bounded volume is shown to be finite under the assumption that all the vertices of a polytope are all in.
Abstract: A lattice polytope is a polytope in whose vertices are all in . The volume of a lattice polytope P containing exactly k ≥ 1 points in d in its interior is bounded above by . Any lattice polytope in of volume V can after an integral unimodular transformation be contained in a lattice cube having side length at most n ˙ n ! V. Thus the number of equivalence classes under integer unimodular transformations of lattice poly topes of bounded volume is finite. If S is any simplex of maximum volume inside a closed bounded convex body K in having nonempty interior, then K ⊆ ( n + 2)S — (n+ l)s where mS denotes a nomothetic copy of S with scale factor m, and s is the centroid of S.
215 citations
1 Jan 2016
TL;DR: This interior point algorithms theory and analysis tends to be the representative book in this website.
Abstract: Spend your few moment to read a book even only few pages. Reading book is not obligation and force for everybody. When you don't want to read, you can get punishment from the publisher. Read a book becomes a choice of your different characteristics. Many people with reading habit will always be enjoyable to read, or on the contrary. For some reasons, this interior point algorithms theory and analysis tends to be the representative book in this website.
112 citations
TL;DR: The research focus of this study presents a development of computational fuzzy topology, which is based on the interior operator and closure operator, and is applicable for computing the values of fuzzy topological relations, such as defined conceptually by the 9-intersection model.
74 citations
TL;DR: In this article, the notions of (ψ, ψ)-open map, gn-continuity and gn-open map were introduced and investigated by using new interior operators defined on generalized neighborhood systems of a nonempty set.
Abstract: We characterize some properties of generalized topological spaces and (g,g’)-continuity by using an interior operator defined on a generalized topological space. Also, we introduce the notions of (ψ, ψ’)-open map, gn-continuity, gn-open map and investigate their properties by using new interior (or closure) operators defined on generalized neighborhood systems of a nonempty set.
67 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 5 |
| 2015 | 4 |
| 2014 | 5 |
| 2013 | 6 |