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

Taras Banakh; Anatolij Plichko

RACSAM (2006)

- Volume: 100, Issue: 1-2, page 31-37
- ISSN: 1578-7303

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topBanakh, Taras, and Plichko, Anatolij. "The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.." RACSAM 100.1-2 (2006): 31-37. <http://eudml.org/doc/41640>.

@article{Banakh2006,

abstract = {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 X with meager hyperspace K(X). Also under (d = c) we construct a metrizable separable noncomplete linear metric space with hereditarily Baire hyperspace. We do not know if such a space can be constructed in ZFC.},

author = {Banakh, Taras, Plichko, Anatolij},

journal = {RACSAM},

keywords = {linear metric spaces; Baire properties; algebraic dimension},

language = {eng},

number = {1-2},

pages = {31-37},

title = {The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.},

url = {http://eudml.org/doc/41640},

volume = {100},

year = {2006},

}

TY - JOUR

AU - Banakh, Taras

AU - Plichko, Anatolij

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

JO - RACSAM

PY - 2006

VL - 100

IS - 1-2

SP - 31

EP - 37

AB - 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 X with meager hyperspace K(X). Also under (d = c) we construct a metrizable separable noncomplete linear metric space with hereditarily Baire hyperspace. We do not know if such a space can be constructed in ZFC.

LA - eng

KW - linear metric spaces; Baire properties; algebraic dimension

UR - http://eudml.org/doc/41640

ER -

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