Hyperbolic geometry in the work of Johann Heinrich Lambert
... attempt to show that such a geometry does not exist. As a matter of fact, these authors were hoping that in examining a geometry based on the negation of Euclid’s parallel axiom,1 one could reach conclusions that would contradict the other Euclidean postulates. The problem of whether the parallel ax ...
... attempt to show that such a geometry does not exist. As a matter of fact, these authors were hoping that in examining a geometry based on the negation of Euclid’s parallel axiom,1 one could reach conclusions that would contradict the other Euclidean postulates. The problem of whether the parallel ax ...
- Journal of Linear and Topological Algebra
... is to define α (µX , µY )-continuous multifunctions and to obtain some characterizations and several properties concerning such multifunctions. Moreover, the relationships between generalized α (µX , µY )-continuous multifunctions and some known concepts are also discussed. ...
... is to define α (µX , µY )-continuous multifunctions and to obtain some characterizations and several properties concerning such multifunctions. Moreover, the relationships between generalized α (µX , µY )-continuous multifunctions and some known concepts are also discussed. ...
A SURVEY OF MAXIMAL TOPOLOGICAL SPACES
... A. Ramanathan [44] characterized the maximal compact spaces as those compact spaces in which the compact subsets are precisely the closed sets, and exhibited a maximal compact space which is not Hausdorff, thus answering Vaidyanathaswamy's question. H. Tong [54] and V. K. Balachandran [4] also obtai ...
... A. Ramanathan [44] characterized the maximal compact spaces as those compact spaces in which the compact subsets are precisely the closed sets, and exhibited a maximal compact space which is not Hausdorff, thus answering Vaidyanathaswamy's question. H. Tong [54] and V. K. Balachandran [4] also obtai ...
Takashi Noiri and Valeriu Popa THE UNIFIED THEORY
... m-space. Each member of mX is said to be mX -open and the complement of an mX -open set is said to be mX -closed. Remark 3.1. (1) An m-structure is equivalent to a generalized topology due to Lugojan [9]. (2) Let (X, τ ) be a topological space. Then the families α(X), SO(X), PO(X) and δ(X) are all m ...
... m-space. Each member of mX is said to be mX -open and the complement of an mX -open set is said to be mX -closed. Remark 3.1. (1) An m-structure is equivalent to a generalized topology due to Lugojan [9]. (2) Let (X, τ ) be a topological space. Then the families α(X), SO(X), PO(X) and δ(X) are all m ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.