A note on metrically inward mappings
A note on minimal dynamical systems
A note on my paper "Notes on compact semigroups with identity".
A note on paratopological groups
In this paper, it is proved that a first-countable paratopological group has a regular -diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [Spaces with a regular -diagonal, Topology Appl. 153 (2006), 1917–1929]. If is a symmetrizable paratopological group, then is a developable space. We also discuss copies of and of in paratopological groups and generalize some Nyikos [Metrizability and the Fréchet-Urysohn property in topological groups, Proc. Amer. Math....
A note on pseudobounded paratopological groups
Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological group....
A note on Rudin's example of Dowker space
A note on some fixed point results.
A note on “Some results on multi-valued weakly Jungck mappings in b-metric space”
The proofs of Theorems 2.1, 2.2 and 2.3 from [Olatinwo M.O., Some results on multi-valued weakly jungck mappings in b-metric space, Cent. Eur. J. Math., 2008, 6(4), 610–621] base on faulty evaluations. We give here correct but weaker versions of these theorems.
A note on strong measure zero sets
A note on the centralizer of topological isometric extensions
The centralizer of a semisimple isometric extension of a minimal flow is described.
A note on the convergence of a pair of sequences of mappings
A note on the minimal essential set of coincident points for set-valued mappings.
A note on the parameters of rational iteration groups.
A note on the Souslin operations
A note on the structure of quadratic Julia sets
In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present...
A note on topological groups and their remainders
In this note we first give a summary that on property of a remainder of a non-locally compact topological group in a compactification makes the remainder and the topological group all separable and metrizable. If a non-locally compact topological group has a compactification such that the remainder of belongs to , then and are separable and metrizable, where is a class of spaces which satisfies the following conditions: (1) if , then every compact subset of the space is a...
A note on topological properties of non-Hausdorff manifolds.
A note on Tsirelson type ideals
Using Tsirelson’s well-known example of a Banach space which does not contain a copy of or , for p ≥ 1, we construct a simple Borel ideal such that the Borel cardinalities of the quotient spaces and are incomparable, where is the summable ideal of all sets A ⊆ ℕ such that . This disproves a “trichotomy” conjecture for Borel ideals proposed by Kechris and Mazur.
A note on -ultrafilters and -points
A note on universal minimal dynamical systems
Let denote the phase space of the universal minimal dynamical system for a group . Our aim is to show that is homeomorphic to the absolute of , whenever is a countable Abelian group.