In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to L-topological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived

We study maximal independent families (hereafter: mifs) and their applications to topological questions. We prove that if there exists either an (ω, ω1)-mif of size 2 ω1 with open density ω, or an (ω, ω1)-mif of size ≤ 2, then there exists an ω-resolvable, not maximally resolvable, Tychonoff space.

In a previous work, we showed that a kind of ω-automata known as Transition-based Generalized Testing Automata (TGTA) can outperform the Büchi automata traditionally used for explicit model checking when verifying stutter-invariant properties. In this work, we investigate the use of these generalized testing automata to improve symbolic model checking of stutter-invariant LTL properties. We pro...

in this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. explicit formulas are givenfor dihedral groups $d_{2n}$, quasi-dihedral groups $qd_{2^n}$, generalized quaternion groups $q_{4n}$ and modular $p$-groups $m_{p^n}$.

Given a bounded open set Ω ⊂ ℝ 2 , we study the relaxation of nonparametric area functional in strict topology BV (Ω; ). and compute it for vortex-type maps, more generally maps W 1,1 (Ω;S 1 ) having finite number topological singularities. We also extend analysis to some specific piecewise constant ), including symmetric triple junction map.

if we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. in this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

The interplay between between gauge-field winding numbers, θ-vacua, and the Dirac operator spectrum in finite-volume gauge theories is reconsidered. To assess the weight of each topological sector, we compare the mass-dependent chiral condensate in gauge field sectors of fixed topological index with the answer obtained by summing over the topological charge. Also the microscopic Dirac operator ...

Slender rings and their products are characterized in terms of algebraic and topological properties. Possible limitations on uncountable products of such rings are discussed. Ring, module, and topological terminology and notation are standard. R denotes a unital ring with identity 1, and R ω denotes its countable product, that is, the set of all sequences of elements of R. Of course ω {0, 1,. ....

Geldenhuys and Hansen showed that a kind of ω-automata known as Testing Automata (TA) can, in the case of stuttering-insensitive properties, outperform the Büchi automata traditionally used in the automata-theoretic approach to model checking [10]. In previous work [23], we compared TA against Transition-based Generalized Büchi Automata (TGBA), and concluded that TA were more interesting when c...

A permutation group G (acting on a set Ω, usually infinite) is said to be oligomorphic if G has only finitely many orbits on Ωn (the set of n-tuples of elements of Ω). Such groups have traditionally been linked with model theory and combinatorial enumeration; more recently their group-theoretic properties have been studied, and links with graded algebras, Ramsey theory, topological dynamics, an...