Related papers: Constructing Compacta from Posets
We introduce and study a family of countable groups constructed from Euclidean buildings by "removing" suitably chosen subsets of chambers.
We discuss conditions under which certain compactifications of topological spaces can be obtained by composing the ultrafilter space monad with suitable reflectors. In particular, we show that these compactifications inherit their…
Every countable topological group $G$ has a closed discrete subset $A$ such that $G=AA^{-1}.$
We give a moderately motivated exposition of exponentiable locales and the construction of exponentials in $\textsf{Loc}$, without assuming prior knowledge of exponential topological spaces or continuous posets.
We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these…
We say that two classes of topological spaces are equivalent if each member of one class has a homeomorphic copy in the other class and vice versa. Usually when the Borel complexity of a class of metrizable compacta is considered, the class…
In the paper, we investigate (scattered) compact spaces with a $P$-base for some poset $P$. More specifically, we prove that, under the assumption $\omega_1<\mathfrak{b}$, any compact space with an $\omega^\omega$-base is first-countable…
We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson. This gives an answer to a…
We construct a path-connected homogenous compactum with cellularity 2^omega that is not homeomorphic to any product of dyadic compacta and first countable compacta. We also prove some closure properties for classes of spaces defined by…
Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].
We associate bicomplexes with the finite Toda lattice and with a finite Toda field theory in such a way that conserved currents and charges are obtained by a simple iterative construction.
There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively…
We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…
We explain how to see finite combinatorics of preorders implicit in the {text} of basic topological definitions or arguments in (Bourbaki, General topology, Ch.I), and define a concise combinatorial notation such that complete definitions…
We study high dimensional expansion beyond simplicial complexes (posets) and focus on $q$-complexes which are complexes whose basic building blocks are linear spaces. We show that the complete $q$-complex (consists of all subspaces of a…
We introduce soft bitopological spaces from the standpoint of soft elements. A soft bitopological space is a soft set equipped with two soft topologies. Following the classical construction of Goldar--Ray, each soft topology on $F$ induces…
Some properties of skelatally generated spaces are established. In particular, it is shown that any compactum co-absolute to a $\kappa$-metrizable compactum is skeletally generated. We also prove that a compactum $X$ is skeletally generated…
We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical…