A study of topological structures on equi-continuous mappings

Gupta, Ankit ^[1] ; Sarma, Ratna Dev ^[1]
1. [1] University of Delhi
  
  University of Delhi
  
  India
Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 2, 2021, págs. 335-354
Idioma: inglés
Títulos paralelos:
- A un estudio de estructuras topológicas en mapeos equi-continuos
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Resumen
- Function space topologies are developed for EC(Y,Z), the class of equi-continuous mappings from a topological space Y to a uniform space Z. Properties such as splittingness, admissibility etc. are defined for such spaces. The net theoretic investigations are carried out to provide characterizations of splittingness and admissibility of function spaces on EC(Y,Z). The open-entourage topology and pointtransitive-entourage topology are shown to be admissible and splitting respectively. Dual topologies are defined. A topology on EC(Y,Z) is found to be admissible (resp. splitting) if and only if its dual is so.