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Realcompactification of frames

Nizar Marcus (1995)

Commentationes Mathematicae Universitatis Carolinae

We give a construction of Wallman-type realcompactifications of a frame L by considering regular sub σ -frames the join of which generates L . In particular, we show that the largest such regular sub σ -frame gives rise to the universal realcompactification of L .

Realcompactness and spaces of vector-valued functions

Jesus Araujo (2002)

Fundamenta Mathematicae

It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T: C*(X,E) → C*(Y,F) is a biseparating...

Rectangular covers of products missing diagonals

Yukinobu Yajima (1994)

Commentationes Mathematicae Universitatis Carolinae

We give a characterization of a paracompact Σ -space to have a G δ -diagonal in terms of three rectangular covers of X 2 ∖ Δ . Moreover, we show that a local property and a global property of a space X are given by the orthocompactness of ( X × β X ) ∖ Δ .

Reflecting character and pseudocharacter

Lucia R. Junqueira, Alberto M. E. Levi (2015)

Commentationes Mathematicae Universitatis Carolinae

We say that a cardinal function φ reflects an infinite cardinal κ , if given a topological space X with φ ( X ) ≥ κ , there exists Y ∈ [ X ] ≤ κ with φ ( Y ) ≥ κ . We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences with...

Reflecting Lindelöf and converging ω₁-sequences

Alan Dow, Klaas Pieter Hart (2014)

Fundamenta Mathematicae

We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ω-sequence or a non-trivial converging ω₁-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of property K posets. In fact in these models every compact Hausdorff space without non-trivial converging ω₁-sequences is first-countable and, in addition,...

Reflexive families of closed sets

Zhongqiang Yang, Dongsheng Zhao (2006)

Fundamenta Mathematicae

Let S(X) denote the set of all closed subsets of a topological space X, and C(X) the set of all continuous mappings f:X → X. A family 𝓐 ⊆ S(X) is called reflexive if there exists ℱ ⊆ C(X) such that 𝓐 = {A ∈ S(X): f(A) ⊆ A for every f ∈ ℱ}. We investigate conditions ensuring that a family of closed subsets is reflexive.

Regular and Other Kinds of Extensions of Topological Spaces

Dimov, G. (1998)

Serdica Mathematical Journal

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.In this paper the notion of SR-proximity is introduced and in virtue of it some new proximity-type descriptions of the ordered sets of all (up to equivalence) regular, resp. completely regular, resp. locally compact extensions of a topological space are obtained. New proofs of the Smirnov Compactification Theorem [31] and of the...

Currently displaying 1381 – 1400 of 1977