Geodesic
Seperation, irreducibility, Urysohn's lemma and Tietze extension theorem for Cauchy spaces
Filomat, Tome 37 (2023) no. 19, p. 6417

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DOI

In this paper, we introduce two notions of closure operators in the category of Cauchy spaces which satisfy (weak) hereditariness, productivity and idempotency, and we characterize each of T i , i = 0, 1, 2 cauchy spaces by using these closure operators as well as show each of these subcategories are isomorphic. Furthermore, we characterize the irreducible Cauchy spaces and examine the relationship among each of irreducible, connected Cauchy spaces. Finally, we present Urysohn's lemma and Tietze extension theorem for Cauchy spaces.
DOI : 10.2298/FIL2319417K
Classification : 54B30, 54D10, 54A05, 54A20, 18B99, 18D15
Keywords: Topological category, Cauchy space, Cauchy map, Separation, Connectedness, Compactness 
Sümeyye Kula; Muammer Kula. Seperation, irreducibility, Urysohn's lemma and Tietze extension theorem for Cauchy spaces. Filomat, Tome 37 (2023) no. 19, p. 6417 . doi: 10.2298/FIL2319417K
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     title = {Seperation, irreducibility, {Urysohn's} lemma and {Tietze} extension theorem for {Cauchy} spaces},
     journal = {Filomat},
     pages = {6417 },
     year = {2023},
     volume = {37},
     number = {19},
     doi = {10.2298/FIL2319417K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2319417K/}
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