A transfinite extension of the covering dimension
A tree -base for without cofinal branches
We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree -base for with no branches yet of height . We establish that this is also possible for using a natural modification of Mathias forcing.
A Tychonoff non-normal space.
A Tychonoff theorem in intuitionistic fuzzy topological spaces.
A type of βN with relative types
A Unified Theory of Perfect and Related Functions
A unified theory of weak separation properties.
A uniform structure for topological spaces
A unique common fixed point theorem for occasionally weakly compatible maps.
A unique factorization theorem for countable products of circles
A uniquely homogeneous space need not be a topological group
A universal metacompact developable -space of weight m
A universal planar completely regular continuum
We construct a universal planar completely regular continuum. This gives a positive answer to a problem posed by J. Krasinkiewicz (1986).
A Universal Proper G-Space.
A universal property of -semigroups
Let be a -semigroup with unbounded generator . We prove that has generically a very irregular behaviour for as .
A universal separable metric locally finite-dimensional space
A variant of a theorem of Sierpiński concerning partitions of continua
A variational problem for couples of functions and multifunctions with interaction between leaves
We discuss a variational problem defined on couples of functions that are constrained to take values into the 2-dimensional unit sphere. The energy functional contains, besides standard Dirichlet energies, a non-local interaction term that depends on the distance between the gradients of the two functions. Different gradients are preferred or penalized in this model, in dependence of the sign of the interaction term. In this paper we study the lower semicontinuity and the coercivity of the energy...
A vector lattice variant of the ergodic theorem
A very general covering property
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are shown to be equivalent to a covering property in the sense considered here (Corollary 3.10). Conversely, every covering property is equivalent to the existence of appropriate kinds of accumulation points for arbitrary sequences on some fixed index set (Corollary 3.5)....