### Electronic Research Archive

2020, Issue 1: 471-548. doi: 10.3934/era.2020027
Special Issues

# Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces

• Received: 01 December 2019 Revised: 01 February 2020
• Primary: 54E15, 54D05; Secondary: 54G15, 54G20

• Motivated by some ordinary and extreme connectedness properties of topologies, we introduce several reasonable connectedness properties of relators (families of relations). Moreover, we establish some intimate connections among these properties.

More concretely, we investigate relationships among various minimalness (well-chainedness), connectedness, hyper- and ultra-connectedness, door, superset, submaximality and resolvability properties of relators.

Since most generalized topologies and all proper stacks (ascending systems) can be derived from preorder relators, the results obtained greatly extends some standard results on topologies. Moreover, they are also closely related to some former results on well-chained and connected uniformities.

Citation: Muwafaq Salih, Árpád Száz. Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces[J]. Electronic Research Archive, 2020, 28(1): 471-548. doi: 10.3934/era.2020027

### Related Papers:

• Motivated by some ordinary and extreme connectedness properties of topologies, we introduce several reasonable connectedness properties of relators (families of relations). Moreover, we establish some intimate connections among these properties.

More concretely, we investigate relationships among various minimalness (well-chainedness), connectedness, hyper- and ultra-connectedness, door, superset, submaximality and resolvability properties of relators.

Since most generalized topologies and all proper stacks (ascending systems) can be derived from preorder relators, the results obtained greatly extends some standard results on topologies. Moreover, they are also closely related to some former results on well-chained and connected uniformities.

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