Is every pseudo-orbit of some homeomorphism near an exact orbit of a nearby homeomorphism?

A notion of graph homeomorphism

We introduce a notion of graph homeomorphisms which uses the concept of dimension and homotopy for graphs. It preserves the dimension of a subbasis, cohomology and Euler characteristic. Connectivity and homotopy look as in classical topology. The Brouwer-Lefshetz fixed point leads to the following discretiszation of the Kakutani fixed point theorem: any graph homeomorphism T with nonzero Lefsch...

A Homeomorphism Invariant for Substitution

We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of Čech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like ti...

Pseudo-tumor of the orbit.

Homeomorphism between [:e

The notation and terminology used in this paper have been introduced in the following articles: [20], [9], [25], [7], [8], [4], [16], [24], [21], [19], [13], [18], [23], [1], [2], [10], [5], [17], [11], [3], [22], [14], [12], [6], [26], and [15]. We use the following convention: i, j, n denote natural numbers, f , g, h, k denote finite sequences of elements of R, and M , N denote non empty metr...

Continuity and Homeomorphism Groups

Proof. There exists an open neighborhood W of xgcb such that clsWCZ U, where els W denotes the closure of W. Let [ATjfc|fe = l, 2, • • • ] be a neighborhood base at ~1 which is closed. Moreover WEW, i.e. 4>UxEW. Thus there exists k such that ATJItCWCcls W. Hence xECk. Now from WlCU...