Remarks on some class of continuous mappings of λ-dendroids
Remarks on some fixed point theorems.
Remarks on some generalizations of asymptotic periodicity in dynamical systems on metric spaces
Remarks on star countable discrete closed spaces
In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming , there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.
Remarks on star covering properties in pseudocompact spaces
Let be a topological property. A space is said to be star if whenever is an open cover of , there exists a subspace with property such that , where In this paper, we study the relationships of star properties for in pseudocompact spaces by giving some examples.
Remarks on Star-Hurewicz Spaces
A space X is star-Hurewicz if for each sequence (𝒰ₙ: n ∈ ℕ) of open covers of X there exists a sequence (𝓥ₙ: n ∈ ℕ) such that for each n, 𝓥ₙ is a finite subset of 𝒰ₙ, and for each x ∈ X, x ∈ St(⋃ 𝓥ₙ,𝒰ₙ) for all but finitely many n. We investigate the relationship between star-Hurewicz spaces and related spaces, and also study topological properties of star-Hurewicz spaces.
Remarks on strongly star-Menger spaces
A space is strongly star-Menger if for each sequence of open covers of , there exists a sequence of finite subsets of such that is an open cover of . In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.
Remarks on subsets of Cartesian products of metric spaces
Remarks on superextensions
Remarks on the absolute suspension
Remarks on the cardinality of a power homogeneous space
We provide a further estimate on the cardinality of a power homogeneous space. In particular we show the consistency of the formula for any regular power homogeneous ccc space.
Remarks on the region of attraction of an isolated invariant set
We study the complexity of the flow in the region of attraction of an isolated invariant set. More precisely, we define the instablity depth, which is an ordinal and measures how far an isolated invariant set is from being asymptotically stable within its region of attraction. We provide upper and lower bounds of the instability depth in certain cases.
Remarks on the sobriety of Scott topology and weak topology on posets
We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].
Remarks on the Stone Spaces of the Integers and the Reals without AC
In ZF, i.e., the Zermelo-Fraenkel set theory minus the Axiom of Choice AC, we investigate the relationship between the Tychonoff product , where 2 is 2 = 0,1 with the discrete topology, and the Stone space S(X) of the Boolean algebra of all subsets of X, where X = ω,ℝ. We also study the possible placement of well-known topological statements which concern the cited spaces in the hierarchy of weak choice principles.
Remarks on topologically algebraic functors
Remarks on topologies uniquely determined by their continuous self maps
Remarks on transfinite diameters
Remarks on weakly KKM maps in abstract convex spaces.
Remarks on Yu’s ‘property A’ for discrete metric spaces and groups
Guoliang Yu has introduced a property on discrete metric spaces and groups, which is a weak form of amenability and which has important applications to the Novikov conjecture and the coarse Baum–Connes conjecture. The aim of the present paper is to prove that property in particular examples, like spaces with subexponential growth, amalgamated free products of discrete groups having property A and HNN extensions of discrete groups having property A.
Remarks to the problem of defining a topology by its homeomorphism group