18 papers
This paper investigates the number of isomorphism types of Banach spaces for compact spaces of a given weight, proving that there are exactly $2^\kappa\kappa\omega_12^{\omega_1}$) depends on additional set-theoretic axioms such as the Continuum Hypothesis or Baumgartner's axiom.
This paper establishes that the natural closure operator on a graph's vertex set, defined by a set and its neighbors, induces a canonical convergence structure, which the authors analyze using nets to relate combinatorial graph properties to convergence-theoretic characteristics.
This paper characterizes the amenability of countable Borel equivalence relations via the uniform Liouville property, investigates Kesten's property for return probabilities on topological groups, and constructs an amenable contractible Polish group lacking this property by linking it to anti-concentration inequalities in measurable lamplighter groups.
This paper establishes that nontrivial automorphisms of the Boolean algebra exist in Cohen extensions of a model for any number of added reals , and extends this result to under additional hypotheses involving sage Davies trees.
This paper generalizes the Peter-Weyl Theorem by demonstrating that functions on locally compact groups with large nontrivial compact open subgroups can be approximated by locally representative functions.
This paper establishes that the family of graphs of real-valued functions contains uncountably many pairwise non-embeddable spaces with specific topological properties, while simultaneously proving that the locally connected members of this family form a countable, linearly ordered chain under embeddability and fully classifying separable, locally connected refinements of the real line's topology.
This paper demonstrates that the Hausdorff distance is a specific instance of a broader family of inter-set distances formed by composing a set-valued function with a real-valued set-function, leading to the construction of adaptable classes of set-valued metrics and generalized Hausdorff distances suitable for most practical applications.
This paper introduces the novel concepts of -contraction and Bianchini -contraction within super metric spaces, proves the existence and uniqueness of their fixed points through nontrivial examples, and applies these theoretical results to model terrain-following airplane navigation.
This paper establishes the descriptive complexity of various mathematical structures by proving that the Hindman ideal, the ideal , and specific families of trees are -complete, while also exploring the connections between ideals on and classical tree types like Sacks and Miller.
This paper establishes the existence of two distinct equilibrium concepts for non-cooperative games under uncertainty—Nash equilibrium with capacity-based mixed strategies and Dow-Werlang equilibrium with non-additive beliefs—by utilizing max-plus integrals and fixed point theorems within an abstract convexity framework.
This paper resolves the open question regarding the parameterized complexity of the Optimal Morse Matching problem by presenting a $2^{O(k \log k)} n$-time algorithm for bounded-treewidth complexes and proving its optimality under the Exponential Time Hypothesis.
This paper introduces an induction-free notion of completeness for topological spaces equipped with a graded base by redefining net convergence as an approach relation, thereby extending classical completeness results from uniform spaces to a broader class of locally symmetric base spaces.
This paper constructs the Extended Real Line with Reentry (ERI), a compact, path-connected, T₁ space that is US but not KC, thereby providing an explicit counterexample that separates these properties in the Wilansky hierarchy while demonstrating that its only continuous real-valued functions are constants.
This paper proves that every locally compact strongly topological gyrogroup possesses a suitable set, thereby affirmatively resolving a question previously posed by F. Lin and colleagues.
This paper establishes that magnitude is continuous on the open and dense subset of skew finite subsets within the space of finite subsets of by deriving explicit weight measure formulas for their cubical thickenings and proving the convergence of their magnitudes.
This paper investigates the Equi-Baire one property for families of Möbius transformations, demonstrating that iterates of loxodromic maps form such a family on their attracting basins and establishing that a one-parameter subgroup satisfies this condition on all compact sets if and only if it is relatively compact in .
This paper employs topological and ergodic perspectives, including thermodynamic formalism and Alexandroff compactification, to prove that the Collatz function possesses a unique cycle with no divergent orbits, while also extending these finiteness and non-divergence results to Baker and Syracuse maps.
This paper investigates the topological structure of Julia continua for disjoint-type transcendental entire functions, characterizing them as arc-like continua with span zero and demonstrating that a single such function can realize any arc-like continuum with a terminal point, while also resolving questions regarding accessibility from the Fatou set and the uniformity of escape to infinity.