Locally fine measurable spaces
Author:
Zdeněk Frolík
Journal:
Trans. Amer. Math. Soc. 196 (1974), 237247
MSC:
Primary 54E15; Secondary 04A15, 28A05
MathSciNet review:
0383357
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Abstract: HyperBaire sets and hypercozero sets in a uniform space are introduced, and it is shown that for metricfine spaces the property ``every hypercozero set is a cozero set'' is equivalent to several much stronger properties like being locally efine (defined in §1), or having locally determined precompact part (introduced in §2). The metricfine spaces with these additional properties form a coreflective subcategory of uniform spaces; the coreflection is explicitly described. The theory is applied to measurable uniform spaces. It is shown that measurable spaces with the additional properties mentioned above are coreflective and the coreflection is explicitly described. The two coreflections are not metrically determined.
 [E]
Čech, Topological spaces, 2nd ed., Publ. House Czech Acad. Sci., Prague, 1966; English transl., Wiley, New York, 1966. MR 35 #2254.
 [Z]
Frolík, [F1] Topological methods in measure theory and the theory of measurable spaces, General Topology and its Relations to Modern Analysis and Algebra (Proc. 3rd Prague Sympos., 1971), Academia, Prague, 1972, pp. 127139. MR 0372141 (51:8358)
 1.
, [F2] Interplay af measurable and uniform spaces, Topology and its Applications (Proc. 2nd Yugoslavia Sympos., Budva, 1972), Beograd, 1973, pp. 9699.
 2.
, [F3] Hyperextensions of algebras, Comment. Math. Univ. Carolinae 14 (1973), 361375. MR 0346115 (49:10841)
 3.
, [F4] A note on metricfine spaces, Proc. Amer. Math. Soc. (to appear). MR 0358704 (50:11163)
 4.
, [F5] Measurable uniform spaces, Pacific J. Math. (to appear), MR 0383358 (52:4239)
 [A]
Hager, [1] Some nearly fine uniform spaces, Proc. London Math. Soc. (to appear). MR 0397670 (53:1528)
 5.
, [2] Measurable uniform spaces, Fund. Math. 77 (1972), 5173. MR 0324661 (48:3011)
 [R]
Hansell, [1] Thesis, Rochester, 1970.
 6.
, [2] On the nonseparable theory of Borel and Souslin sets, Bull. Amer. Math. Soc. 78 (1972), 236241. MR 45 #3211. MR 0294138 (45:3211)
 [J]
Isbell, Uniform spaces, Math. Surveys, no. 12, Amer. Math. Soc., Providence, R. I., 1964. MR 30 #561 MR 0170323 (30:561)
 [E]
 Čech, Topological spaces, 2nd ed., Publ. House Czech Acad. Sci., Prague, 1966; English transl., Wiley, New York, 1966. MR 35 #2254.
 [Z]
 Frolík, [F1] Topological methods in measure theory and the theory of measurable spaces, General Topology and its Relations to Modern Analysis and Algebra (Proc. 3rd Prague Sympos., 1971), Academia, Prague, 1972, pp. 127139. MR 0372141 (51:8358)
 1.
 , [F2] Interplay af measurable and uniform spaces, Topology and its Applications (Proc. 2nd Yugoslavia Sympos., Budva, 1972), Beograd, 1973, pp. 9699.
 2.
 , [F3] Hyperextensions of algebras, Comment. Math. Univ. Carolinae 14 (1973), 361375. MR 0346115 (49:10841)
 3.
 , [F4] A note on metricfine spaces, Proc. Amer. Math. Soc. (to appear). MR 0358704 (50:11163)
 4.
 , [F5] Measurable uniform spaces, Pacific J. Math. (to appear), MR 0383358 (52:4239)
 [A]
 Hager, [1] Some nearly fine uniform spaces, Proc. London Math. Soc. (to appear). MR 0397670 (53:1528)
 5.
 , [2] Measurable uniform spaces, Fund. Math. 77 (1972), 5173. MR 0324661 (48:3011)
 [R]
 Hansell, [1] Thesis, Rochester, 1970.
 6.
 , [2] On the nonseparable theory of Borel and Souslin sets, Bull. Amer. Math. Soc. 78 (1972), 236241. MR 45 #3211. MR 0294138 (45:3211)
 [J]
 Isbell, Uniform spaces, Math. Surveys, no. 12, Amer. Math. Soc., Providence, R. I., 1964. MR 30 #561 MR 0170323 (30:561)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197403833579
PII:
S 00029947(1974)03833579
Article copyright:
© Copyright 1974
American Mathematical Society
