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Modifications of the double arrow space and related Banach spaces C(K)

Witold Marciszewski (2008)

Studia Mathematica

We consider the class of compact spaces K A which are modifications of the well known double arrow space. The space K A is obtained from a closed subset K of the unit interval [0,1] by “splitting” points from a subset A ⊂ K. The class of all such spaces coincides with the class of separable linearly ordered compact spaces. We prove some results on the topological classification of K A spaces and on the isomorphic classification of the Banach spaces C ( K A ) .

Monotone extenders for bounded c-valued functions

Kaori Yamazaki (2010)

Studia Mathematica

Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, C ( A , c ) the set of all bounded continuous functions f: A → c, and C A ( X , c ) the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender u : C ( A , c ) C A ( X , c ) . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question...

Monotone meta-Lindelöf spaces

Yin-Zhu Gao, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

In this paper, we study the monotone meta-Lindelöf property. Relationships between monotone meta-Lindelöf spaces and other spaces are investigated. Behaviors of monotone meta-Lindelöf G O -spaces in their linearly ordered extensions are revealed.

More on ordinals in topological groups

Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (2008)

Commentationes Mathematicae Universitatis Carolinae

Let τ be an uncountable regular cardinal and G a T 1 topological group. We prove the following statements: (1) If τ is homeomorphic to a closed subspace of G , G is Abelian, and the order of every non-neutral element of G is greater than 5 then τ × τ embeds in G as a closed subspace. (2) If G is Abelian, algebraically generated by τ G , and the order of every element does not exceed 3 then τ × τ is not embeddable in G . (3) There exists an Abelian topological group H such that ω 1 is homeomorphic to a closed subspace...

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