-directed inverse systems of continuous images of arcs.
-Dowker spaces
-Hausdorff biclosure spaces.
1/2-Homogeneous hyperspace suspensions
We continue the study of 1/2-homogeneity of the hyperspace suspension of continua. We prove that if X is a decomposable continuum and its hyperspace suspension is 1/2-homogeneous, then X must be continuum chainable. We also characterize 1/2-homogeneity of the hyperspace suspension for several classes of continua, including: continua containing a free arc, atriodic and decomposable continua, and decomposable irreducible continua about a finite set.
3-dimensional AR's which do not contain 2-dimensional ANR's
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