In this paper we introduce a new class of closed maps namely g#s-closed also homeomorphisms called g#s*-homeomorphisms and prove that the set all form group under operation composition maps.

Let $$f:X\rightarrow X$$ be a hereditarily locally connected continuum homeomorphism and denote respectively by P(f), AP(f) $$\Omega (f)$$ , the sets of periodic points, almost points non-wandering f. We show that any $$\omega $$ -limit set (resp. $$\alpha set) is minimal. Moreover, we (f)=AP(f)$$ . also prove if $$P(f)=\emptyset then there exists unique minimal set. On other hand, $$P(f)\ne \e...

The notion of a parabolic Cantor set is introduced allowing in the definition of hyperbolic Cantor sets some fixed points to have derivatives of modulus one. Such difference in the assumptions is reflected in geometric properties of these Cantor sets. It turns out that if the Hausdorff dimension of this set is denoted by h, then its h-dimensional Hausdorff measure vanishes but the h-dimensional...

A homeomorphism f : X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x 6= y, then there is an integer n ∈ Z such that d(fn(x), fn(y)) > c. A homeomorphism f : X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ Z such that diam fn(A) > c. Clearly, every expansive homeom...