| Autor: |
DURMISHI, Emin, MISAJLESKI, Zoran, SADIKU, Flamure, IBRAIMI, Alit |
| Předmět: |
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| Zdroj: |
Journal of Natural Sciences & Mathematics (JNSM); 2023, Vol. 8 Issue 15/16, p365-368, 4p |
| Abstrakt: |
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 chain V 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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