For a set X of vertices of a graph fulllling a local connectedness condition results on the existence of paths and cycles containing X are given.

Interrelations between smoothness of a continuum at a point, pointwise smoothness, the property of Kelley at a point and local connectedness are studied in the paper.

New types of connectedness in $ S $-proximity spaces, named as an $-$\delta$-connectedness, local $-$ \delta $-connectedness are introduced. Also, their inter-relationships studied. In space (X, \delta_{X}) $, the a subset U X with respect to \delta_{X} may not be same its subspace proximity \delta_{U} $. Further, $-component and $-treelike spaces also defined number results given.

We use the Shokurov connectedness principle and the Corti inequality to prove the birational superrigidity of a nodal hypersurface in P 5 of degree 5. We assume that all varieties are projective, normal and defined over C.

The construction of new urban roads may cause severance, or the separation of residents from local amenities or social networks. Using qualitative data from a natural experimental study, we examined severance related to a new section of urban motorway constructed through largely deprived residential neighbourhoods in Glasgow, Scotland. Semi-structured and photo-elicitation interviews were used ...

An uncountable collection of uniformly arcwise connected plane Suslinian dendroids is constructed which shows that the negations of the following properties: local connectedness, smoothness, pointwise smoothness, hereditary contractibility, and selectibility are not countable in this class of

In this paper, we construct an object, called a system of approximate roots of a valuation, centered in a regular local ring, which describes the fine structure of the valuation (namely, its valuation ideals and the graded algebra). We apply this construction to valuations associated to a point of the real spectrum of a regular local ring A. We give two versions of the construction: the first, ...