We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabili...

We show that if a domain Ω in a geodesic metric space is quasimöbius to a uniform domain in some metric space, then Ω is also uniform. Mathematics Subject Classification (2000). 30C65

The standard proof of the uniform convexity of L using Clarkson’s [1] or Hanner’s [2] inequalities (see also [4]) is rarely taught in functional analysis classes, in part (the author imagines) because the proofs of those inequalities are quite non-intuitive and unwieldy. We present here a direct proof, cheerfully sacrificing the optimal bounds – for which, see [2, 4]. It fits quite nicely in wi...

To support human recollection, we present a data integration method using a simple information structure called a history structure, which is constructed from time, keywords, and URI sets. We also present algorithms that generate history structures from such information usages as Web searches, twitter, e-mails, calendars, and book purchases and create a user knowledge space. Based on our approa...

We prove that a generic canonically or bicanonically embedded smooth curve has semistable m Hilbert points for all m ≥ 2. We also prove that a generic bicanonically embedded smooth curve has stable m Hilbert points for all m ≥ 3. In the canonical case, this is accomplished by proving finite Hilbert semistability of special singular curves with Gm-action, namely the canonically embedded balanced...

A subset A of the state space is called uniformly globally weakly attractive if for any neighborhood S of A and any bounded subset B there is a uniform finite time τ so that any trajectory starting in B intersects S within the time not larger than τ . We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attracti...