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A proof for the Blair-Hager-Johnson theorem on absolute z -embedding

Kaori Yamazaki (2002)

Commentationes Mathematicae Universitatis Carolinae

In this paper, a simple proof is given for the following theorem due to Blair [7], Blair-Hager [8] and Hager-Johnson [12]: A Tychonoff space X is z -embedded in every larger Tychonoff space if and only if X is almost compact or Lindelöf. We also give a simple proof of a recent theorem of Bella-Yaschenko [6] on absolute embeddings.

An example related to strongly pointwise self-homeomorphic dendrites

Pavel Pyrih (1999)

Archivum Mathematicum

Such spaces in which a homeomorphic image of the whole space can be found in every open set are called self-homeomorphic. W.J. Charatonik and A. Dilks posed a problem related to strongly pointwise self-homeomorphic dendrites. We solve this problem negatively in Example 2.1.

An independency result in connectification theory

Alessandro Fedeli, Attilio Le Donne (1999)

Commentationes Mathematicae Universitatis Carolinae

A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let ψ be the following statement: “a perfect T 3 -space X with no more than 2 𝔠 clopen subsets is connectifiable if and only if no proper nonempty clopen subset of X is feebly compact". In this note we show that neither ψ nor ¬ ψ is provable in ZFC.

An observation on Krull and derived dimensions of some topological lattices

M. Rostami, Ilda I. Rodrigues (2011)

Archivum Mathematicum

Let ( L , ) , be an algebraic lattice. It is well-known that ( L , ) with its topological structure is topologically scattered if and only if ( L , ) is ordered scattered with respect to its algebraic structure. In this note we prove that, if L is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then L has Krull-dimension if and only if L has derived dimension. We also prove the same result for error L , the set of all prime elements of L . Hence the dimensions on the lattice...

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