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.
A note on transfinite dimension
A note on transitively -spaces
In this note, we show that if for any transitive neighborhood assignment for there is a point-countable refinement such that for any non-closed subset of there is some such that , then is transitively . As a corollary, if is a sequential space and has a point-countable -network then is transitively , and hence if is a Hausdorff -space and has a point-countable -network, then is transitively . We prove that if is a countably compact sequential space and has a point-countable...
A note on zero-dimensional preimages of compact spaces
A note on -closed sets and inverse limits.
A note to decompositions of real line
A partically ordered space which is not a Priestely space.
A positional characterization of the (n-1)-dimensional Sierpiński curve in (η ≠ 4)
A Product Theorem in Dimension.
A property of the Sorgenfrey line
A Pullback theorem for cofibrations.
A Pullback Theorem for Locally-Equiconnected Spaces.
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
A remark on the equivalence of certain dimension functions
A remark on the Moore theorem.
A retractible non-locally connected dendroid
A retractible non-locally connected dendroid is constructed.