In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to R that is globally Hölder continuous of exponent α ∈ (0, 1], and whose inverse is also globally Hölder continuous of exponent α can be approximated in the Hölder norm of exponent β by pi...

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold homeomorphism types. This is a generalization to the orbifold category of a similar result for manifolds proven by Grove, Petersen, and Wu. It follows that any Laplace ...

In this paper we give a method of constructing homeomorphisms between two small covers over simple convex polytopes. As a result we classify, up to homeomorphism, all small covers over a 3-dimensional prism P(m) with m ≥ 3. We introduce two invariants from colored prisms and two invariants from ordinary cohomology ring, which form a complete invariant system of homeomophism types of all small c...

Let M be a separable compact Hausdorff space with dim M ≤ 2 and θ : M → M be a homeomorphism with prime period p (p ≥ 2). Set Mθ = {x ∈ M | θ(x) = x} 6= ∅ and M0 = M\Mθ. Suppose that M0 is dense in M and H(M0/θ,Z) ∼= 0, H(χ(M0/θ),Z) ∼= 0. Let M ′ be another separable compact Hausdorff space with dim M ′ ≤ 2 and θ′ be the self–homeomorphism of M ′ with prime period p. Suppose that M ′ 0 = M ′\M ...

It is shown that the homeomorphism groups of the (generalized) Sierpiński carpet and the universal Menger continua are not zero-dimensional. These results were corollaries to a 1966 theorem of Brechner. New proofs were needed because we also show that Brechner’s proof is inadequate. The method by which we obtain our results, the construction of closed imbeddings of complete Erdős space in the h...

We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to Kn (n ≥ 3), Km,n (m,n ≥ 2), and wheels Wr (r ≥ 3). Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs. We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some speci...