The aim of this paper is to introduce the notion of $ \delta $-connectedness modulo an ideal in proximity spaces. A sufficient condition for a $ \delta $-connected modulo an ideal proximity space to be connected modulo an ideal is defined. The notion of $ \delta $-connectedness modulo a proximal property is defined, and several results for $ \delta $-connectedness modulo compactness and modulo pseudocompactness are obtained. $ \delta $-perfect map for proximity spaces is defined and it is shown that the class of $ \delta $-perfect maps is properly contained in the class of perfect maps, and some results about $ \delta $-perfect maps are substantiated.
Citation: Beenu Singh, Davinder Singh. $ \delta $-connectedness modulo an ideal[J]. AIMS Mathematics, 2022, 7(10): 17954-17966. doi: 10.3934/math.2022989
The aim of this paper is to introduce the notion of $ \delta $-connectedness modulo an ideal in proximity spaces. A sufficient condition for a $ \delta $-connected modulo an ideal proximity space to be connected modulo an ideal is defined. The notion of $ \delta $-connectedness modulo a proximal property is defined, and several results for $ \delta $-connectedness modulo compactness and modulo pseudocompactness are obtained. $ \delta $-perfect map for proximity spaces is defined and it is shown that the class of $ \delta $-perfect maps is properly contained in the class of perfect maps, and some results about $ \delta $-perfect maps are substantiated.
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Beenu Singh, Davinder Singh. $ \delta $-connectedness modulo an ideal[J]. AIMS Mathematics, 2022, 7(10): 17954-17966. doi: 10.3934/math.2022989
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