A graph G is locally connected if the subgraph induced by the neighbourhood of each vertex is connected. We prove that a locally connected graph G of order p 3, containing no induced subgraph isomorphic to K 1;3 , is Hamilton-connected if and only if G is 3-connected.

We obtain a number of consequences of the theorem on the automatic continuity of locally bounded finite-dimensional representations of connected Lie groups on the derived subgroup of the group, as well as an analogue of Lie’s theorem for (not necessarily continuous) finite-dimensional representations of connected soluble locally compact groups. In particular, we give a description of connected ...

AMS no. 30F40 The main result here is the fact that the limit set of a geometrically finite Kleinian group with connected limit set is locally connected. For an analytically finite Kleinian group with connected limit set, we give necessary and sufficient conditions for the limit set to be locally connected.

In this paper, we provide a characterization as to when a locally connected generalized continuum (a locally compact connected separable metric space) has a countable compactiication of a certain order type. We then prove that for any two locally connected generalized continua with maximal countable compactiications X and Y of the same order type there is a perfect surjection f : X ! Y. This pr...

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...

A detailed structure theorem is shown for locally compact, locally connected, hereditarily normal spaces and for normal, locally compact, locally connected, hereditarily ω1-scwH spaces in models of PFA(S)[S], and for the latter kinds of spaces in models of PFA. Corollaries include a powerful refinement theorem like that for monotonically normal spaces, and the corollary that the spaces involved...

A general path-lifting theorem, which fails in the context of topological spaces, is shown to hold for toposes, for locales (a slight generalization of topological spaces), and hence for complete separable metric spaces. This result generalizes the known fact that any connected locally connected topos (respectively complete separable metric space) is path-connected. In [MW] we proved that every...

Let G be a graph. For each vertex v 2V (G), Nv denotes the subgraph induces by the vertices adjacent to v inG. The graphG is locally k edge-connected if for each vertex v 2V (G), Nv is k-edge-connected. In this paper we study the existence of nowhere-zero 3-flows in locally k-edgeconnected graphs. In particular, we show that every 2-edge-connected, locally 3-edge-connected graph admits a nowher...