in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

which is part of a certain 2d Hamiltonian cohomological field theory [11]. Here we use this map to study the topology of ΩHam(M, ω) and its Hofer geometric properties via a kind of virtual Morse theory for the positive Hofer length functional, L : ΩHam(M, ω) → R . We also use Ψ to prove a kind of index theorem for some critical points of L . We apply this theory to get some concrete application...

Since Chang [2] introduced fuzzy theory into topology, many authors have discussed various aspects of fuzzy topology. It is well known that weakly induced and induced topological spaces play an important role in L-topological spaces (see book [8]). According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly impo...

Let X be a hypergroup. In this paper, we define a locally convex topology β on L(X) such that (L(X), β) with the strong topology can be identified with a Banach subspace of L(X). We prove that if X has a Haar measure, then the dual to this subspace is LC(X) ∗∗ = cl{F ∈ L(X);F has compact carrier}. Moreover, we study the operators on L(X) and L 0 (X) which commute with translations and convoluti...

In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...

References 1. C. E. Capel, Inverse limit spaces, Duke Math. J. vol. 21 (1954) pp. 233-246. 2. H. Hahn, Mengentheoretische Charakterisierung der stetigen Kurve, Sitzungsber. Akad. Wiss., Wien, vol. 123 (1914) pp. 2433-2489. 3. J. L. Kelley, General topology, New York, van Nostrand Co., 1955. 4. S. Mazurkiewicz, Sur les lignes de Jordan, Fund. Math. vol. 1 (1920) pp. 166209. 5. R. L. Wilder, Topo...

We give a thorough overview of the different notions for order convergence that are found in literature and provide systematic comparison associated topologies. As an application this study we prove result related to topology on von Neumann algebras, complementing started Chetcuti et al. (Stud. Math. 230:95-120, 2015). show every atomic algebra (not necessarily \(\sigma \)-finite) restriction b...

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

Assuming that the underlying probability space is non-atomic we prove that products of random matrices (linear cocycles) with simple Lyapunov spectrum form an L p-dense set (1 p < 1) in the space of all cocy-cles satisfying the integrability conditions of the multiplicative ergodic theorem. However, the linear cocycles with one-point spectrum are also L p-dense. Further, in any L 1-neighborhood...