The composition of two previously introduced Galois connections is used to provide a wider perspective on the Clementino-Tholen connectedness versus separation Galois connection. Moreover, a link between this and Castellini’s connectedness-disconnectednes Galois connection is also presented.

Let T be the attractor of injective contractions f1, . . . , fm on R 2 that satisfy the Open Set Condition. If T is connected, ∂T is arcwise connected. In particular, the boundary of the Lévy dragon is arcwise connected.

The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z 7! z2 + c. We prove that the tricorn is not locally connected and not even pathwise connected, confirming an observation of John Milnor from 1992. We extend this discussion more generally for antiholomorphic unicritical polynomials of degrees d 2 and their connectedness loci, known as multicorns.

We consider a nonconvex and nonclosed higher order differential inclusion and we prove the arcwise connectedness of the solution set.

ofThe Transcendental Critique Revisited and Revised Dooyeweerd’s account of abstraction is examined and found to be faulty. He holds that abstract thinkingisolates aspects which must then be synthesized, whereas I argue that we cannot isolate any aspect from the othershowever so hard we try. But our very inability to isolate aspects is then turned into an alternative version of ...

It is known that connectedness is one of the important notions in topology. In this paper, a new notion of connectedness is introduced in L-topological spaces, which is called PS-connectedness. It contains some nice properties. Especially, the famous K. Fan’s Theorem holds for PS-connectedness in L-topological spaces.

We use the Shokurov connectedness principle and the Corti inequality to prove the birational superrigidity of a nodal hypersurface in P 5 of degree 5. We assume that all varieties are projective, normal and defined over C.

Yeshun Sun & Yongcheng Yin [3] and H. Ishida & T. Itoh [2] presented a precise description of the real cross section of the connectedness locus of the family of bi-quadratic polynomials {(z2+a)2+b}. In this note, we shall give a precise description of the real cross section of the connectedness locus of the family of polynomials {(P2n+1,b ◦P2n+1,a)(z)} = {(z2n+1 + a)2n+1 + b}, where a, b are co...

We prove that any unicritical polynomial fc : z 7→ z+c which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies that the connectedness locus (the “Multibrot set”) is locally connected at the corresponding parameter values. It generalizes Yoccoz’s Theorem for quadratics to the higher degree case. Stony Brook IMS Preprint #2005/05 July 2005