| Autor: |
Shekutkovski, Nikita, Misajleski, Zoran, Durmishi, Emin |
| Předmět: |
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| Zdroj: |
ROMAI Journal; 2021, Vol. 17 Issue 2, p73-80, 8p |
| Abstrakt: |
In [4] the definition of connectedness of a topological space is reformulated by using the notion of chain and proved its equivalence to the standard definition of connectedness. In [2] and [5] the definition of connectedness by using the notion of chain is generalized to the notion of chain connected set in a topological space. Here it is proved that the product of chain connected sets in their corre-sponding spaces is a chain connected set in the product space equipped with the product topology. Thus, by using the notion of chain, it is proved that the product of connected spaces is a connected space equipped with the product topology. Since every connected set is chain connected in every its superspace, it is obvious that the product of some chain connected sets in their corresponding spaces with some connected subsets of their corresponding spaces is a chain connected set in the product space equipped with the product topology. How-ever, by a counterexample it is shown that this product may be disconnected. By counterexample it is shown that the product of chain connected sets in their corresponding spaces may not be a chain connected set in the product space equipped with the box topology. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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