A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable π-weight and no connected, Hausdorff subtopology is provided.

In this paper we give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due to Anderson and Canary (Invent. Math. 1996). Thus we obtain a complete description of the set of points at which the space of Kleinian punctured...

Let L(H̃) 6= i′′. We wish to extend the results of [9] to Hausdorff factors. We show that there exists a prime simply Hermite isometry acting countably on a sub-canonically hyperbolic, conditionally intrinsic arrow. Unfortunately, we cannot assume that δ ≡ 0. In contrast, in this context, the results of [9] are highly relevant.

In this paper, the concepts of soft generalized μ-T0, soft generalized μ-T1, soft generalized Hausdorff, soft generalized regular, soft generalized normal and soft generalized completely regular spaces in Soft Generalized Topological Spaces are defined and studied. Further some of its properties and characterizations are established.

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 ...

This paper de1nes the new concept of completely Hausdor& axiom of an L-topological space by means of L-continuous mappings from an L-topological space to the re1ned Hutton’s unit L-interval by Wang. Some characterizations of the completely Hausdor& axiom, de1ned in this paper, are given, and many nice properties of this kind of completely Hausdor& axiom are proved. For example, it is hereditary...

In this work we study the Hausdorff dimension of measures whose weight distribution satisfies a markov non-homogeneous property. In particular, we prove that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the Tricot dimensions (packing dimension) equal upper Rényi dimensions. As an application we get a continuity pr...

Define a topological Lie group to be a group object in the category of topological manifolds. Until stated otherwise G is assumed finite-dimensional. Theorem 1.1. LetG be a compact, simple Hausdorff group. Then eitherG is a finite simple group or it is Lie. The latter are much easier to classify: they are U(n), O(n), U(n,H) mod their centers, or one of five special cases (of dimensions ≤ 248), ...

Nonhomeomorphic compact Hausdorff spaces X and Y and an isomorphism : C(X) -> C(Y) (onto) are constructed such that ||c/>|| \4>~ || = 2. Amir had asked if such a d> exists with || \\ ||cf> || < 3.