Algunos resultados sobre anillos de Wallman.
Almost convex metrics and Peano compactifications.
An interesting class of ideals in subalgebras of containing
In the present paper we give a duality between a special type of ideals of subalgebras of containing and -filters of by generalization of the notion -ideal of . We also use it to establish some intersecting properties of prime ideals lying between and . For instance we may mention that such an ideal becomes prime if and only if it contains a prime ideal. Another interesting one is that for such an ideal the residue class ring is totally ordered if and only if it is prime.
An internal characterization of WI spaces
Approach merotopological spaces and their completion.
Approximation theorems for compactifications
We shall show several approximation theorems for the Hausdorff compactifications of metrizable spaces or locally compact Hausdorff spaces. It is shown that every compactification of the Euclidean n-space ℝⁿ is the supremum of some compactifications homeomorphic to a subspace of . Moreover, the following are equivalent for any connected locally compact Hausdorff space X: (i) X has no two-point compactifications, (ii) every compactification of X is the supremum of some compactifications whose remainder...
Approximations of Stone-Cech compactifications by Higson compactifications
Behavior of biharmonic functions on Wiener's and Royden's compactifications
Let be a smooth Riemannian manifold of finite volume, its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of are found, and for biharmonic functions (those for which ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.
Biframe compactifications
Compactifications of biframes are defined, and characterized internally by means of strong inclusions. The existing description of the compact, zero-dimensional coreflection of a biframe is used to characterize all zero-dimensional compactifications, and a criterion identifying them by their strong inclusions is given. In contrast to the above, two sufficient conditions and several examples show that the existence of smallest biframe compactifications differs significantly from the corresponding...
Binding spaces: A unified completion and extension theory
Bohr compactifications of discrete structures
We prove the following theorem: Given a⊆ω and , if for some and all u ∈ WO of length η, a is , then a is .We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: -Turing-determinacy implies the existence of .
Cardinal invariants and compactifications
We prove that every compact space is a Čech-Stone compactification of a normal subspace of cardinality at most , and some facts about cardinal invariants of compact spaces.
Categories of topological spaces with sufficiently many sequentially closed spaces
Categories of Wallman extendible functions
Cauchy Spaces. II. Regular Completions and Compactifications.
Čech complete nearness spaces
We study Čech complete and strongly Čech complete topological spaces, as well as extensions of topological spaces having these properties. Since these two types of completeness are defined by means of covering properties, it is quite natural that they should have a convenient formulation in the setting of nearness spaces and that in that setting these formulations should lead to new insights and results. Our objective here is to give an internal characterization of (and to study) those nearness...
Čech-completeness and ultracompleteness in “nice spaces”
We prove that if is a union of subspaces of pointwise countable type then the space is of pointwise countable type. If is a countable union of ultracomplete spaces, the space is ultracomplete. We give, under CH, an example of a Čech-complete, countably compact and non-ultracomplete space, giving thus a partial answer to a question asked in [BY2].
Čech-Stone-like compactifications for general topological spaces
The problem whether every topological space has a compactification such that every continuous mapping from into a compact space has a continuous extension from into is answered in the negative. For some spaces such compactifications exist.
Čechův-Stoneův -obal
Circle spaces