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The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.

Taras Banakh, Anatolij Plichko (2006)

RACSAM

Answering a question of Halbeisen we prove (by two different methods) that the algebraic dimension of each infinite-dimensional complete linear metric space X equals the size of X. A topological method gives a bit more: the algebraic dimension of a linear metric space X equals |X| provided the hyperspace K(X) of compact subsets of X is a Baire space. Studying the interplay between Baire properties of a linear metric space X and its hyperspace, we construct a hereditarily Baire linear metric space...

The dimension of metrizable subspaces of Eberlein compacta and Eberlein compactifications of metrizable spaces

Michael G. Charalambous (2004)

Fundamenta Mathematicae

We prove that every Baire subspace Y of c₀(Γ) has a dense $G_{δ}$ metrizable subspace X with dim X ≤ dim Y. We also prove that the Kimura-Morishita Eberlein compactifications of metrizable spaces preserve large inductive dimension. The proofs rely on new and old results concerning the dimension of uniform spaces.

The Dimension Print of Most Convex Surfaces.

Tudor Zamfirescu, G. Craciun (1997)

Monatshefte für Mathematik

The Dugundji extension property can fail in ωµ -metrizable spaces

Ian Stares, Jerry Vaughan (1996)

Fundamenta Mathematicae

We show that there exist $ω_{μ}$ -metrizable spaces which do not have the Dugundji extension property ( $2^{ω_{1}}$ with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.

The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces

Harold Bennett, David Lutzer (2013)

Fundamenta Mathematicae

We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically normal spaces....

The LCC-topology on the space of continuous functions

Jaromír Šiška (1982)

Commentationes Mathematicae Universitatis Carolinae

The $α$ -completion of a lattice ordered group

Richard N. Ball, Gary Davis (1983)

Czechoslovak Mathematical Journal

Tilings in topological spaces.

Arenas, F.G. (1999)

International Journal of Mathematics and Mathematical Sciences

Topological zero-one laws

K. P. S. Bhaskara Rao, Roman Pol (1978)

Colloquium Mathematicae

Topologies in product which preserve Baire spaces

Anna Kucia (1990)

Commentationes Mathematicae Universitatis Carolinae

Two generic results in fixed point theory

Simeon Reich, Alexander J. Zaslavski (2007)

Banach Center Publications

We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansive mappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finite-dimensional Euclidean spaces.

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