A metrization theorem for the product of ordered continua
A new ordered compactification.
A non-chainable plane continuum with span zero
A plane continuum is constructed which has span zero but is not chainable.
A non-metrizable collectionwise Hausdorff tree with no uncountable chains and no Aronszajn subtrees
It is independent of the usual (ZFC) axioms of set theory whether every collectionwise Hausdorff tree is either metrizable or has an uncountable chain. We show that even if we add “or has an Aronszajn subtree,” the statement remains ZFC-independent. This is done by constructing a tree as in the title, using the set-theoretic hypothesis , which holds in Gödel’s Constructible Universe.
A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension
We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.
A non-zero dimensional atom in the lattice of uniformities
A note on cardinal invariants of square
A note on cyclic subelement theory-reducibility of local connectedness and local simple connectedness
A note on dimension theory of metric spaces
A note on embeddings manifolds into topological groups preserving dimensions
A note on inverse limits of continuous images of arcs.
The main purpose of this paper is to prove some theorems concerning inverse systems and limits of continuous images of arcs. In particular, we shall prove that if X = {Xa, pab, A} is an inverse system of continuous images of arcs with monotone bonding mappings such that cf (card (A)) ≠ w1, then X = lim X is a continuous image of an arc if and only if each proper subsystem {Xa, pab, B} of X with cf(card (B)) = w1 has the limit which is a continuous image of an arc (Theorem 18).
A note on open mappings of irreducible continua
A note on ordered planes.
A note on singular homology groups of infinite products of compacta
Let n be an integer with n ≥ 2 and be an infinite collection of (n-1)-connected continua. We compare the homotopy groups of with those of (Σ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the n(≥ 2)-sphere is given.
A note on the dimension Dind
A note on the homotopical characterization of Rn.
A note on the isomorphic classification of spaces of continuous functions defined on intervals of ordinal numbers
A note on the paper ``Smoothness and the property of Kelley''
Let be a continuum. In Proposition 31 of J.J. Charatonik and W.J. Charatonik, Smoothness and the property of Kelley, Comment. Math. Univ. Carolin. 41 (2000), no. 1, 123–132, it is claimed that , where is the set of points at which is locally connected and, for , if and only if is smooth at with respect to . In this paper we show that such equality is incorrect and that the correct equality is , where is the set of points at which is connected im kleinen. We also use the correct...
A note on topological m-spaces
A note on topology of -continuous posets
-continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of -continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a -continuous poset is defined and its properties are explored.