Add to ORKGThe paper presents some theorems about interlaced spheres of different dimensions in multidimensional spaces. Two spheres Sk and Sm are called interlaced with each other if their intersection is empty, however, one of them crosses each topological ball whose boundary is the other sphere. We describe a method of simulating interlaced spheres in computer. We demonstrate the connection between the notion of a tunnel in a multidimensional "body", i.e. in a connected subset of a multidimensional space, and that of interlaced spheres. Examples of multidimensional tunnels in four- and five-dimensional spaces are demonstrated. 1
AbstractAs shown by D. Barnette (1973, J. Combin. Theory Ser. A14, 37–53) there are precisely 39 sim...
In this paper we establish an analogue of the Fary-Milnor Theorem for space-like 2-spheres in Minkow...
Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. T...
We characterize those unions of embedded disjoint circles in the sphere (Formula presented.) which c...
It is possible to make interwoven structures by using two or more surfaces with holes. Several solut...
Although our everyday perception of space tells us that it is composed of three spatial dimensions o...
This project highlights the connections between elastic spaces, known as topological spaces, and spa...
Interlocking puzzles are very challenging geometric problems with the fascinating property that once...
We show that any embedding of the n-skeleton of a (2n+ 3)-dimensional simplex into the (2n + 1)-dime...
In the article, based on the philosophical analysis of the concept of "three-dimensional space", a m...
On an Interesting Interpenetration --The sphere and the torus will he shown to intersect in a real ...
We construct some examples of finite and infinite crystalline three-dimensional nets derived from sy...
Abstract. Let L be a non-split, prime and alternating link in the 3-sphere S3, and S an incompressib...
There is a long history to the study of locally flat and locally tame embeddings of manifolds. A few...
Cheeger’s finiteness theorem bounds the number of diffeomorphism types of manifolds with bounded cur...
AbstractAs shown by D. Barnette (1973, J. Combin. Theory Ser. A14, 37–53) there are precisely 39 sim...
In this paper we establish an analogue of the Fary-Milnor Theorem for space-like 2-spheres in Minkow...
Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. T...
We characterize those unions of embedded disjoint circles in the sphere (Formula presented.) which c...
It is possible to make interwoven structures by using two or more surfaces with holes. Several solut...
Although our everyday perception of space tells us that it is composed of three spatial dimensions o...
This project highlights the connections between elastic spaces, known as topological spaces, and spa...
Interlocking puzzles are very challenging geometric problems with the fascinating property that once...
We show that any embedding of the n-skeleton of a (2n+ 3)-dimensional simplex into the (2n + 1)-dime...
In the article, based on the philosophical analysis of the concept of "three-dimensional space", a m...
On an Interesting Interpenetration --The sphere and the torus will he shown to intersect in a real ...
We construct some examples of finite and infinite crystalline three-dimensional nets derived from sy...
Abstract. Let L be a non-split, prime and alternating link in the 3-sphere S3, and S an incompressib...
There is a long history to the study of locally flat and locally tame embeddings of manifolds. A few...
Cheeger’s finiteness theorem bounds the number of diffeomorphism types of manifolds with bounded cur...
AbstractAs shown by D. Barnette (1973, J. Combin. Theory Ser. A14, 37–53) there are precisely 39 sim...
In this paper we establish an analogue of the Fary-Milnor Theorem for space-like 2-spheres in Minkow...
Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. T...