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Functional separation of inductive limits and representation of presheaves by sections. I: Separation theorems for inductive limits of closured presheaves. (English) Zbl 0421.54012


MSC:

54C30 Real-valued functions in general topology
54A05 Topological spaces and generalizations (closure spaces, etc.)
54B30 Categorical methods in general topology
54E05 Proximity structures and generalizations
54E15 Uniform structures and generalizations
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
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References:

[1] N. Bourbaki: Elements de Mathématique. Livre III, Topologie Generale, Paris, Hermann, 1951. · Zbl 0042.09201
[2] G. E. Bredon: Sheaf Theory. McGraw-Hill, New York, 1967. · Zbl 0158.20505
[3] E. Čech: Topological Spaces. Prague, 1966. · Zbl 0141.39401
[4] J. Dauns K. H. Hofmann: Representation of Rings by Sections. Mem. Amer. Math., Soc, 83 (1968). · Zbl 0174.05703
[5] J. Dugundji: Topology. Allyn and Bacon, Boston, 1966. · Zbl 0144.21501
[6] Z. Frolík: Structure Projective and Structure Inductive Presheaves. Celebrazioni archimedee del secolo XX, Simposio di topologia, 1964.
[7] A. N. Gelfand D. A. Rajkov G. E. Silov: Commutative Normed Rings. Moscow, 1960
[8] E. Hille, Ralph S. Phillipps: Functional Analysis and Semi-Groups. Providence, 1957.
[9] J. L. Kelley: General Topology. Van Nostrand, New York, 1955. · Zbl 0066.16604
[10] G. Koethe: Topological Vector Spaces, I. New York Inc, Springer Vlg, 1969. · Zbl 0179.17001
[11] G. J. Minty: On the Extension of Lipschitz-Hölder continuous, and Monotone Functions. Bulletin of the A.M.S., 76, (1970), I. · Zbl 0191.34603 · doi:10.1090/S0002-9904-1970-12466-1
[12] J. Pechanec-Drahoš: Representation of Presheaves of Semiuniformisable Spaces, and Representation of a Presheaf by the Presheaf of All Continuous Sections in its Covering Space. Czech. Math. Journal, 21 (96)) · Zbl 0225.54007
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