Consider an involution T of the sphere S without fixed points. Is the quotient manifold S/T necessarily isomorphic to projective nspace? This question makes sense in three different categories. One can work either with topological manifolds and maps, with piecewise linear manifolds and maps, or with differentiable manifolds and maps. For n^3 the statement is known to be true (Livesay [6]). In t...

The distance functions on the set of Keplerian orbits play an important role in solving problems searching for parent bodies meteoroid streams. A special kind function is distances quotient spaces orbits. Three metrics this type were developed earlier. These allow disregarding longitude ascending node or argument pericenter, both. Here, we introduce one more space, where two are considered to b...

This paper deals with the geometry of the space (GIT quotient) M8 of 8 points in P, and the Gale-quotient N ′ 8 of the GIT quotient of 8 points in P. The space M8 comes with a natural embedding in P, or more precisely, the projectivization of the S8-representation V4,4. There is a single S8-skew cubic C in P. The fact that M8 lies on the skew cubic C is a consequence of Thomae’s formula for hyp...

We show that the tangle space of a graph, which compactifies it, is quotient its Stone-Čech remainder obtained by contracting connected components.

‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness...