The convexity of the subset space of a metric space
The covering dimension of product of generalized Sorgenfrey lines
The dimension of hyperspaces of non-metrizable continua
We prove that, for any Hausdorff continuum X, if dim X ≥ 2 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then either dim C(X) = 2 or C(X) is not a C-space. This generalizes some results known for metric continua.
The Dimension of the Set of All Finite Subsets of the Continuum
The (dis)connectedness of products of Hausdorff spaces in the box topology
In this paper the following two propositions are proved: (a) If , , is an infinite system of connected spaces such that infinitely many of them are nondegenerated completely Hausdorff topological spaces then the box product can be decomposed into continuum many disjoint nonempty open subsets, in particular, it is disconnected. (b) If , , is an infinite system of Brown Hausdorff topological spaces then the box product is also Brown Hausdorff, and hence, it is connected. A space is Brown if...
The duality between lattice-ordered monoids and ordered topological spaces.
The envelope of a subcategory in topology and group theory.
The Freudenthal space for approximate systems of compacta and some applications.
In this paper we define a space σ(X) for approximate systems of compact spaces. The construction is due to H. Freudenthal for usual inverse sequences [4, p. 153–156]. We establish the following properties of this space: (1) The space σ(X) is a paracompact space, (2) Moreover, if X is an approximate sequence of compact (metric) spaces, then σ(X) is a compact (metric) space (Lemma 2.4). We give the following applications of the space σ(X): (3) If X is an approximate system of continua, then X = limX...
The functor of weakly additive functionals of finite degree.
The functor σ²X
We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.
The -topology and incompactness of
We establish a relation between covering properties (e.gĿindelöf degree) of two standard topological spaces (Lemmas 4 and 5). Some cardinal inequalities follow as easy corollaries.
The hyperspace of finite subsets of a stratifiable space
It is shown that the hyperspace of non-empty finite subsets of a space X is an ANR (an AR) for stratifiable spaces if and only if X is a 2-hyper-locally-connected (and connected) stratifiable space.
The hyperspace of lower semicontinuity and the first power of a topological space
The indexed open covering theorem
The irreducibility of continua which are the inverse limit of a collection of Hausdorff arcs
The kernel operation on subsets of a -space
The LCC-topology on the space of continuous functions
The lifting property for classes of mappings.
The Lindelöf property and pseudo--compactness in spaces and topological groups
We introduce and study, following Z. Frol’ık, the class of regular -spaces such that the product is pseudo--compact, for every regular pseudo--compact -space . We show that every pseudo--compact space which is locally is in and that every regular Lindelöf -space belongs to . It is also proved that all pseudo--compact -groups are in . The problem of characterization of subgroups of -factorizable (equivalently, pseudo--compact) -groups is considered as well. We give some necessary...
The meet of locally connected group topologies.