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New PDF release: Encyclopedia of General Topology

By Jun-iti Nagata, Klaas Pieter Hart, Jerry E. Vaughan

ISBN-10: 0444503552

ISBN-13: 9780444503558

This ebook is designed for the reader who desires to get a common view of the terminology of normal Topology with minimum effort and time. The reader, whom we imagine to have just a rudimentary wisdom of set conception, algebra and research, should be capable of finding what they wish in the event that they will correctly use the index. even if, this publication includes only a few proofs and the reader who desires to research extra systematically will locate sufficiently many references within the booklet.

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J. 10 (1943), 309–333. J. D. McCartan, Singular sets and maximal topologies, Proc. Amer. Math. Soc. 127 (11) (1998), 3375–3382. E. Larson, Minimal T0 -spaces and maximal TD spaces, Pacific J. Math. 31 (1969), 451–458. D. E. McCluskey, Minimal structures for TFA , Rend. Istit. Mat. Univ. Trieste 27 (1995), 11–24. E. S. Watson, Minimal TU D spaces, Appl. Gen. Topology 3 (1) (2002), 55–64. S. Parhomenko, Über eineindeutige stetige Abbildungen, Mat. Sb. 5 (47) (1939), 197–210 (in Russian). 27 [13] J.

If X is a set, then we use F(X) to denote the set of all filters on X. If Φ : Y → F(X) is a map and F ∈ F(Y ), then Φ(F ) = Φ(y) ∈ F(X) F ∈F y∈F is the sum or contour of Φ over F ; in other words, A ∈ Φ(F ) whenever there exists F ∈ F such that A ∈ Φ(y) for every y ∈ F . A subset ξ of F(X)×X is called a filter convergence (or a convergence structure) on a set X provided that (F , x) ∈ ξ and F ⊂ G imply (G, x) ∈ ξ and (x, ˙ x) ∈ ξ for every x ∈ X, where x˙ stands for the principal filter of {x}. If (F , x) ∈ ξ , then we say that F converges to x (x is a limit of F ) with respect to ξ .

Kopperman, Which topologies are quasimetrizable? Topology Appl. 52 (1993), 99–107. [8] R. Kopperman, Asymmetry and duality in topology, Topology Appl. 66 (1995), 1–39. P. Lane, Bitopological spaces and quasi-uniform spaces, Proc. London Math. Soc. 17 (1967), 341–346. [10] J. Marin and S. Romaguera, A bitopological view of quasi-topological groups, Indian J. Pure Appl. Math. 27 (1996), 393–405. W. Patty, Bitopological spaces, Duke Math. J. 34 (1967), 387–391. G. L. Reilly, On non-symmetric topological structures, Colloq.

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Encyclopedia of General Topology by Jun-iti Nagata, Klaas Pieter Hart, Jerry E. Vaughan

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