In this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎We study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

On the space l of p-summable sequences (of real numbers), one can derive a norm from the 2-norm as indicated by Gunawan [6]. The purpose of this note is to establish the equivalence between such a norm and the usual norm on l. We show that our result is useful in understanding the topology of l as a 2-normed space.

the purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. this is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.

Root system architecture (RSA) plays an important role in plant development and survival. The ability to accurately model and quantify properties of root architecture is fundamental for sustainability studies, crop improvement, and studies of plant-microbal interactions. Existing methods to model RSA either require a dense set of images or rely on 3D scanning methods for dense reconstruction. I...

An arrangement L of k pairwise non-parallel lines in the complex hyperbolic plane H(C) has a link at infinity K∞(L) comprising k unknotted circles in S, whose topology reflects the combinatorics of L “at infinity”. Many links at infinity are far from being fibered; but if L = C LR is the complexification of a connected hyperbolic R-line arrangement LR ⊂ H(R), then K∞(L) is fibered. §

We give an example of a subspaceK of L∞(Ω,F ,P) such thatK∩L+ = {0}, where K denotes the closure with respect to convergence in probablity. On the other hand, the cone C := K−L+ is dense in L∞ with respect to the weak-star topology σ(L∞, L1). This example answers a question raised by I. Evstigneev. The topic is motivated by the relation of the notion of no arbitrage and the existence of marting...

the aim of the present paper is to define and study (ic)$lm$-fuzzytopological spaces, a generalization of (weakly) induced $lm$-fuzzytopological spaces. we discuss the basic properties of(ic)$lm$-fuzzy topological spaces, and introduce the notions ofinterior (ic)-fication and exterior (ic)-fication of $lm$-fuzzytopologies and prove that {bf iclm-ftop} (the category of(ic)$lm$-fuzzy topological ...

In previous work [J. D. Skufca and E. Bollt, Mathematical Biosciences and Engineering, 1 (2004), pp. 347–359], empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static ...