Topological categories containing any category of algebras
Topological characterization of the small cardinal
We show that the small cardinal number is a maximal independent family} has the following topological characterization: has a dense irresolvable countable subspace}, where denotes the Cantor cube of weight . As a consequence of this result, we have that the Cantor cube of weight has a dense countable submaximal subspace, if we assume (ZFC plus ), or if we work in the Bell-Kunen model, where and .
Topological compactifications
We study those compactifications of a space such that every autohomeomorphism of the space can be continuously extended over the compactification. These are called H-compactifications. Van Douwen proved that there are exactly three H-compactifications of the real line. We prove that there exist only two H-compactifications of Euclidean spaces of higher dimension. Next we show that there are 26 H-compactifications of a countable sum of real lines and 11 H-compactifications of a countable sum of Euclidean...
Topological completeness of first countable Hausdorff spaces II
Topological completeness of first countable Hausdorff spaces I
Topological conditional entropy
Topological conditions for bound-2 isomorphisms of C(X)
We establish the topological relationship between compact Hausdorff spaces X and Y equivalent to the existence of a bound-2 isomorphism of the sup norm Banach spaces C(X) and C(Y).
Topological conditions for the existence of fixed points
Topological conjugacy of Morse flows over finite Abelian groups
Topological considerations in the foundations of quantum and time theories
Topological Continuous Convergence.
Topological contraction principle
Topological convergence and uniform convergence
Topological degree and Sperner's lemma
Topological degree theory in fuzzy metric spaces
The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved....
Topological degrees of set-valued compact fields in locally convex spaces [Book]
Topological difference posets
Topological disjointness from entropy zero systems
The properties of topological dynamical systems which are disjoint from all minimal systems of zero entropy, , are investigated. Unlike the measurable case, it is known that topological -systems make up a proper subset of the systems which are disjoint from . We show that has an invariant measure with full support, and if in addition is transitive, then is weakly mixing. A transitive diagonal system with only one minimal point is constructed. As a consequence, there exists a thickly syndetic...
Topological dynamics and the extension of Lyapunov's method
Topological Dynamics of Transformations Induced on the Space of Probability Measures.