A Boolean view of sequential compactness
A -continuum is metrizable if and only if it admits a Whitney map for .
A categorical account of the localic closed subgroup theorem
Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.
A categorical concept of completion of objects
We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.
A categorical guide to separation, compactness and perfectness.
A categorical proof of the equivalence of local compactness and exponentiability in locale theory
A chainable continuum not homeomorphic to an inverse limit on [0, 1] with only one bonding map
A characterization of closed maps using the Whyburn construction.
A characterization of dendroids by the n-connectedness of the Whitney levels
Let X be a continuum. Let C(X) denote the hyperspace of all subcontinua of X. In this paper we prove that the following assertions are equivalent: (a) X is a dendroid, (b) each positive Whitney level in C(X) is 2-connected, and (c) each positive Whitney level in C(X) is ∞-connected (n-connected for each n ≥ 0).
A class of spaces whose Cartesian product with every hereditarily Lindelöf space in Lindelöf
A completion functor for Cauchy groups.
A conglomerate of exponential supercategories of the category of finitely generated topological spaces.
A construction of a CW-decomposition of s-cubes which are manifolds
A construction of the projective modification for a closure-set of a presheaf
A constructive proof of the Tychonoff's theorem for locales
A continuum such that is not continuously homogeneous
A metric continuum is said to be continuously homogeneous provided that for every two points there exists a continuous surjective function such that . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum such that the hyperspace of subcontinua of , , is not continuously homogeneous.
A Corson compact L-space from a Suslin tree
The completion of a Suslin tree is shown to be a consistent example of a Corson compact L-space when endowed with the coarse wedge topology. The example has the further properties of being zero-dimensional and monotonically normal.
A countably compact, separable space which is not absolutely countably compact
We construct a space having the properties in the title, and with the same technique, a countably compact topological group which is not absolutely countably compact.
A counterexample concerning products in the shape category
We exhibit a metric continuum X and a polyhedron P such that the Cartesian product X × P fails to be the product of X and P in the shape category of topological spaces.
A decomposition theorem for a class of continua for which the set function T is continuous
We prove a decomposition theorem for a class of continua for which F. B.. Jones's set function 𝓣 is continuous. This gives a partial answer to a question of D. Bellamy.