Fragmentability of open sets and topological games

Choban Mitrofan; Kenderov Petar; Revalski Julian Petrov

Conţinutul numărului revistei

Articolul precedent

Articolul urmator

513

SM ISO690:2012

CHOBAN, Mitrofan, KENDEROV, Petar, REVALSKI, Julian Petrov. Fragmentability of open sets and topological games. In: Topology and its Applications, 2020, nr. 275, p. 0. ISSN 0166-8641. DOI: https://doi.org/10.1016/j.topol.2019.107004

EXPORT metadate:
Google Scholar
Crossref
CERIF

DataCite
Dublin Core

Topology and its Applications

Numărul 275 / 2020 / ISSN 0166-8641

Fragmentability of open sets and topological games

DOI:https://doi.org/10.1016/j.topol.2019.107004

Pag. 0-0

Choban Mitrofan¹, Kenderov Petar², Revalski Julian Petrov²

¹ Tiraspol State University,
² Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,

Disponibil în IBN: 13 octombrie 2020

Rezumat

We give internal and external characterizations of the topological spaces X in which there exists a metric d (not necessarily generating the topology of X) which fragments the nonempty open sets. I.e. every nonempty open subset contains open subsets of arbitrarily small d-diameter. One of the characterizations says that every such space X is the union of two disjoint sets X₁ and X₂ where X₁ is of the first Baire category in X and X₂ admits a continuous one-to-one mapping into a metrizable space. An external characterization is obtained via the existence of a winning strategy for one of the players in a topological game similar to the Banach-Mazur game. An example of a space X is exhibited for which neither of the players in this game has a winning strategy. Of special interest is the case when the metric d which fragments the nonempty open sets of X is complete and generates a topology finer than the topology of X. This happens if and only if X contains a dense completely metrizable subset.

Cuvinte-cheie
Baire category, Dense completely metrizable subset, Fragmentability of sets, Topological game, Winning strategy

Crossref XML Export

<?xml version='1.0' encoding='utf-8'?>
<doi_batch version='4.3.7' xmlns='http://www.crossref.org/schema/4.3.7' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.crossref.org/schema/4.3.7 http://www.crossref.org/schema/deposit/crossref4.3.7.xsd'>
<head>
<doi_batch_id>ibn-111684</doi_batch_id>
<timestamp>1713502082</timestamp>
<depositor>
<depositor_name>Information Society Development Instiute, Republic of Moldova</depositor_name>
<email_address>idsi@asm.md</email_address>
</depositor>
</head>
<body>
<journal>
<journal_metadata>
<full_title>Topology and its Applications</full_title>
<issn media_type='print'>01668641</issn>
</journal_metadata>
<journal_issue>
<publication_date media_type='print'>
<year>2020</year>
</publication_date>
<issue>275</issue>
</journal_issue>
<journal_article publication_type='full_text'><titles>
<title>Fragmentability of open sets and topological games</title>
</titles>
<contributors>
<person_name sequence='first' contributor_role='author'>
<given_name>Mitrofan</given_name>
<surname>Cioban</surname>
</person_name>
<person_name sequence='additional' contributor_role='author'>
<given_name>Petar</given_name>
<surname>Kenderov</surname>
</person_name>
<person_name sequence='additional' contributor_role='author'>
<given_name>Julian Petrov</given_name>
<surname>Revalski</surname>
</person_name>
</contributors>
<publication_date media_type='print'>
<year>2020</year>
</publication_date>
<pages>
<first_page>0</first_page>
<last_page>0</last_page>
</pages>
<doi_data>
<doi>10.1016/j.topol.2019.107004</doi>
<resource>http://www.crossref.org/</resource>
</doi_data>
</journal_article>
</journal>
</body>
</doi_batch>