Homeomorphisms between finite powers of topological spaces

Properties of β∗-Homeomorphisms in Topological Spaces

The concept of β∗-homeomorphisms is introduced and investigated by Palanimani [13] earlier. In the present paper we investigate some more properties of β∗-homeomorphisms and also investigate contra β∗-homeomorphisms.

Finite Topological Spaces

(1) Let A be a set and f be a finite sequence of elements of 2A. Suppose that for every natural number i such that 1 i and i < len f holds πi f πi+1 f : Let i, j be natural numbers. If i j and 1 i and j len f ; then πi f π j f : (2) Let A be a set and f be a finite sequence of elements of 2A. Suppose that for every natural number i such that 1 i and i< len f holds πi f πi+1 f : Let i, j be natu...

On Topological and Linear Homeomorphisms of Certain Function Spaces

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.

Finite Topological Spaces

Powers of Homeomorphisms with Almost Periodic Properties

Let X be a topological space (an "accessible space," a "1-space," or a " TV-space " in the terminology of Fréchet, Kuratowski, or Alexandroff-Hopf, respectively) and let f(X) = X be a homeomorphism. We use the following terminology, which was suggested by G. A. Hedlund and which is to be carefully distinguished from those terminologies used by Birkhoff, Ayres, Whyburn, and others. A point x of ...