Totally divergent dense sets in Cantor cubes
Totally non-remote points in
Totally nonremote points in are constructed. The number of these points is .
Totally proper forcing and the Moore-Mrówka problem
We describe a totally proper notion of forcing that can be used to shoot uncountable free sequences through certain countably compact non-compact spaces. This is almost (but not quite!) enough to produce a model of ZFC + CH in which countably tight compact spaces are sequential-we still do not know if the notion of forcing described in the paper can be iterated without adding reals.
Totally real submanifolds of with parallel second fundamental form
Tower extension of topological constructs
Let be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct , called the tower extension of (indexed by ). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process has a lot...
Trägertopologien auf meßbaren Räumen.
Trajectories, first return limiting notions and rings of -connected and iteratively -connected functions
In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted ) contained between the families (widely described in literature) of Darboux Baire 1 functions () and connectivity functions (). The solutions to our problems are based, among other, on the suitable construction of the ring,...
Trajectory of the turning point is dense for a co-σ-porous set of tent maps
It is known that for almost every (with respect to Lebesgue measure) a ∈ [√2,2] the forward trajectory of the turning point of the tent map with slope a is dense in the interval of transitivity of . We prove that the complement of this set of parameters of full measure is σ-porous.
Transducer, generalized relays and their characterization
Transfer positive hemicontinuity and zeros, coincidences, and fixed points of maps in topological vector spaces.
Transfinite cardinal dimension and separability
Transfinite inductions producing coanalytic sets
A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a condition which can be easily applied in such situations. We reprove the classical results and as a new application we show that consistently there exists an uncountable coanalytic subset of the plane that intersects every C¹ curve in a countable set.
Transfinite methods in metric fixed-point theory.
Transfinite metrics, sequences and topological properties
Transformation groupoids and bundles of Banach spaces
Transformation groups with no equicontinuous minimal set
Transition operator characterizations of compact and maximally almost periodic locally compact groups.
Transitive flows on manifolds.
In this paper we characterize manifolds (topological or smooth, compact or not, with or without boundary) which admit flows having a dense orbit (such manifolds and flows are called transitive) thus fully answering some questions by Smith and Thomas. Name
Transitivity and partial order
In this paper we find a one-to-one correspondence between transitive relations and partial orders. On the basis of this correspondence we deduce the recurrence formula for enumeration of their numbers. We also determine the number of all transitive relations on an arbitrary -element set up to .
Transitivity in uniform approach theory.