We present two examples of nice normal spaces X having the property that for some xed-point free homeomorphism on X its Cech-Stone extension has a xed point. One of the spaces presented here is locally countable, locally compact, separable , normal, countably paracompact and weakly zero-dimensional. The other one is hereditarily normal and strongly zero-dimensional. Our construction of this exa...

Fixed points play a central role in domain theory, where, traditionally, the least-xed-point operator for continuous endofunctions on complete partial orders (cpos) is used. Recently, there has been considerable interest in developing a more general axiomatic (and order-free) account of the constructions of domain theory. Peter Freyd made an essential contribution to this programme by emphasisi...

We show that the Weyl group W = M 0 =M of a noncompact semisimple Lie group is obtained by taking xed point sets of smooth involutions in K=M. More precisely, one considers rst the xed point set X of the involutions deened on K=M by the elements of order 2 in exp ia. The Weyl group is either X , or the xed point set of the involutions deened on X by special elements of order 4 in exp ia.

In this article, we study the existence of tripled coincidence and tripled common fixed point theorems in partially ordered complete quasi-metric spaces for nonlinear contraction condition related to Q-function q. Our results generalize and modify several comparable results in the literature. We also provide illustrative examples in support of our new results. Mathematics Subject Classification...

Let f be a quadratic polynomial which has an irrationally indi erent xed point Let z be a biaccessible point in the Julia set of f Then In the Siegel case the orbit of z must eventually hit the critical point of f In the Cremer case the orbit of z must eventually hit the xed point Siegel polynomials with biaccessible critical point certainly exist but in the Cremer case it is possible that biac...

We prove that the period doubling operator has an expanding di rection at the xed point We use the induced operator a Perron Frobenius type operator to study the linearization of the period dou bling operator at its xed point We then use a sequence of linear operators with nite ranks to study this induced operator The proof is constructive One can calculate the expanding direction and the rate ...