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The Hahn-Banach theorem in a category of sheaves. (English) Zbl 0438.46051


MSC:

46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
18B25 Topoi
46M10 Projective and injective objects in functional analysis
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References:

[1] Banaschewski, B., Sheaves of Banach spaces, Quaestiones mathematicae, 2, 1-22, (1977) · Zbl 0435.46051
[2] C.W. Burden and C.J. Mulvey, Normed spaces in a topos, to appear. · Zbl 0432.46066
[3] Kantorovich, L.V.; Akilov, G.P., Functional analysis in normed spaces, (1964), Pergamon Press London · Zbl 0127.06104
[4] Mulvey, C.J., Intuitionistic algebra and representations of rings, Mem. amer. math. soc., 148, 3-57, (1974) · Zbl 0274.18012
[5] Mulvey, C.J., Banach sheaves, J. pure applied algebra, 17, (1980) · Zbl 0475.18007
[6] C.J. Mulvey, The real numbers in a topos, to appear.
[7] Staples, J., On constructive fields, Proc. London math. soc., 23, 3, 753-768, (1971) · Zbl 0238.02029
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