DURMISHI, Emin and MISAJLESKI, Zoran and SADIKU, Flamure and IBRAIMI, Alit
(2023)
*CHAIN OF A SET IN A COVERING AND CHAIN COMPONENTS
UP TO A COVERING.*
Journal of Natural Sciences and Mathematics of UT, 8 (15-16).
pp. 365-368.
ISSN 2545-4072

Text
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## Abstract

A chain in the open covering V of a topological space X that joins U V and V V is a finite sequence of elements of V such that U is the first member, V is the last member and every two consecutive members of the sequence have a nonempty intersection. By chainV,V V it is meant the union of all elements of the covering for which there are chains joining them with V and chainV is the set that consists of all sets chainV for each V V. A chain in V that joins x X and y X is a finite sequence of elements of V such that x is contained in the first element of the sequence, y is contained in the last element and every two consecutive elements of the sequence have a nonempty intersection. A V -chain component of an element x X , Ch x( , ), V is the set that consists of all y X such that there exists a chain in V that joins x and y . We prove that chainV Ch x ( , ) V for any V V and any x V , hence chainV consists of V -chain components. As a consequence, chain connectedness is characterized using the chainV notion.

Item Type: | Article |
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Uncontrolled Keywords: | Chain, Star of a set, Open covers, Chain connectedness. |

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |

Depositing User: | Unnamed user with email zshi@unite.edu.mk |

Date Deposited: | 05 Nov 2023 00:09 |

Last Modified: | 05 Nov 2023 00:09 |

URI: | http://eprints.unite.edu.mk/id/eprint/1538 |

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