In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

In this paper the concept of unbounded Fredholm operators on Hilbert C∗modules over an arbitrary C∗-algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Feredholm operators on Hilbert C∗-modules over C∗-algebras of compact operators. In the framework of Hilbert C∗-modules over C∗-algebras of compact operators, the index of an unbounded Fredholm operator and the...

Hofmann and Morris [6] proved that a locally compact connected group G has a finite subset generating a dense subgroup if and only if the weight w(G) of G does not exceed c , the cardinality of the continuum. The minimum cardinality of such a topological generating set is an invariant of the group, is denoted by σ(G), and is called the topological rank of G . For compact abelian groups of weigh...

We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and having only finite boundary smoothness is considerably more complicated than the classification of such domains that have infinitely smooth boundary. Let D ⊂...

We investigate attractors for compact sets by considering a certain quotient space. The following theorem is included. Let /: G -> G, G a closed convex subset of a Banach space, / a mapping satisfying (i) there exists M c G which is an attractor for compact sets under/; (ii) the family {/"}Ü°_i is equicontinuous. Then/has a fixed point. 1. Since the appearance of the celebrated Schauder fixed p...

Let G be a compact definable C group, X a compact affine definable CG manifold and 2 ≤ r < ∞. We prove that the set of equivariant definable Morse functions on X whose loci are finite unions of nondegenerate critical orbits is open and dense in the set of G invariant definable C functions with respect to the definable C topology.

Let X be a countable metric space which is not locally compact. We prove that the function space C,,(X) is homeomorphic to rr,, We also give examples of countable metric spaces X and Y which are not locally compact and such that C,,(X) and C,,(Y) are not linearly homeomorphic.

In this paper i, j, k, n denote natural numbers. Next we state several propositions: (1) For all subsets A, B of E T such that A is Bounded or B is Bounded holds A ∩ B is Bounded. (2) For all subsets A, B of E T such that A is not Bounded and B is Bounded holds A \ B is not Bounded. (3) For every compact connected non vertical non horizontal subset C of E2 T holds (W-min L̃(Cage(C, n))) " Cage(C...

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups of functionals on a C∗-bialgebra, the noncommutative counterpart of a locally compact semigroup. On locally compact quantum groups we obtain a bijective cor...