We are here dealing with the problem of space layout planning. We present an approach based on an intermediate topological level with dynamic space ordering (dso) heuristics. Our software ARCHiPLAN proceeds through a number of steps. First, all the topologically different solutions, without presuming any precise dimension, are enumerated. Next, we may evolve in this topological solution space, ...

Definition 1 (compare [2,5,8]) A topological space is called a KC-space provided that each compact set is closed. A topological space is called a U S-space provided that each convergent sequence has a unique limit. Remark 1 Each Hausdorff space (= T 2-space) is a KC-space, each KC-space is a U S-space and each U S-space is a T 1-space (that is, singletons are closed); and no converse implicatio...

Topological relations are one of the most fundamental properties between spatial objects. The topological relations between crisp spatial objects have been well identified. However how to formalise the topological relations between fuzzy regions needs more investigation. The paper starts from introduction of boundaries defined in the fuzzy topological space. By use of a definition formally equi...

During the last decade, a lot of progress has been made in the enumerative branch of topological graph theory. Enumeration formulas were developed for a large class of graph covering projections. The purpose of this paper is to count graph covering projections of graphs such that the corresponding covering space is a connected graph. The main tool of the enumeration is Pólya’s theorem.

We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from overlap Dirac operator organizes into an ordered space-time structure. It was pointed out that, among other properties, this structure exhibits two important features: it is lowdimensional and geometrically global, i.e. consisting of ...

We establish topological properties of the topological symmetric inverse semigroup of finite transformations I n λ of the rank 6 n. We show that the topological inverse semigroup I n λ is algebraically closed in the class of topological inverse semigroups. Many topologists established topological property of topological spaces of partial continuous maps PC (X, Y ) from a topological space X int...