Finite cartesian product of chain connected sets in topological spaces

Shekutkovski Nikita; Misajleski Zoran; Durmishi Emin

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2022-09-27 22:03

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SHEKUTKOVSKI, Nikita, MISAJLESKI, Zoran, DURMISHI, Emin. Finite cartesian product of chain connected sets in topological spaces. In: Conference on Applied and Industrial Mathematics: CAIM 2021, 17-18 septembrie 2021, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2021, Ediţia a 28-a, p. 54.

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Conference on Applied and Industrial Mathematics
Ediţia a 28-a, 2021

Conferința "Conference on Applied and Industrial Mathematics"
Iași, România, Romania, 17-18 septembrie 2021

Finite cartesian product of chain connected sets in topological spaces

Pag. 54-54

Shekutkovski Nikita¹, Misajleski Zoran¹, Durmishi Emin²

¹ Ss. Cyril and Methodius University in Skopje,
² University of Tetova

Disponibil în IBN: 21 septembrie 2022

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Rezumat

In [1] the de nition of connectedness of a topological space is reformulated by using the notion of chain and proved its equivalence to the standard de nition of connectedness. The topological space X is connected if for every x; y 2 X and for any open covering U of X, there exists a chain in U that connects x and y, i.e., there exists a nite sequence U1;U2;...;Un of elements of U such that x 2 U1, y 2 Un and every two consecutive elements from the chain have nonempty intersection.

Cuvinte-cheie
connectedness, coverings, chain, chain connecteness, cartesian product

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