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.
A short proof of Parovičenko's theorem
A simplified formula for calculation of metric dimension of converging sequences
A singular plane curve
A somewhat surprising subspace of
A study of universal elements in classes of bases of topological spaces
The universality problem focuses on finding universal spaces in classes of topological spaces. Moreover, in “Universal spaces and mappings” by S. D. Iliadis (2005), an important method of constructing such universal elements in classes of spaces is introduced and explained in details. Simultaneously, in “A topological dimension greater than or equal to the classical covering dimension” by D. N. Georgiou, A. C. Megaritis and F. Sereti (2017), new topological dimension is introduced and studied, which...