Page 1 Next

Displaying 1 – 20 of 33

Showing per page

Decompositions of cyclic elements of locally connected continua

D. Daniel (2010)

Colloquium Mathematicae

Let X denote a locally connected continuum such that cyclic elements have metrizable G δ boundary in X. We study the cyclic elements of X by demonstrating that each such continuum gives rise to an upper semicontinuous decomposition G of X into continua such that X/G is the continuous image of an arc and the cyclic elements of X correspond to the cyclic elements of X/G that are Peano continua.

Diagonal conditions in ordered spaces

Harold Bennett, David Lutzer (1997)

Fundamenta Mathematicae

For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each T X 2 - Δ ( X ) with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If ω 1 D ( X ) then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization theorems...

Currently displaying 1 – 20 of 33

Page 1 Next