Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
inverse systems; (gauged) approximate systems; inverse limits; (gauged) approximate resolutions; compact metric spaces
inverse systems; (gauged) approximate systems; inverse limits; (gauged) approximate resolutions; compact metric spaces
Summary:
An approximate inverse sequence of plane continua is constructed which negatively answers a question of S. Marde\v si'c related to approximate and usual inverse systems. The example also shows that an important result of M.G. Charalambous cannot be improved. As an application, it is shown that a procedure of making an approximate inverse sequence commutative (``taming'') is discontinuous.
References:
[1] Charalambous M.G.: Approximate inverse systems of uniform spaces and an application of inverse systems. Comment. Math. Univ. Carolinae 32 (1991), 551-565. MR 1159801 | Zbl 0785.54016
[2] Mardešić S.: On approximate inverse systems and resolutions. to appear in Fund. Math. MR 1220551
[3] Mardešić S., Rubin L.R.: Approximate inverse systems of compacta and covering dimension. Pacific J. Math. 138 (1989), 129-144. MR 0992178
[4] Mardešić S., Segal J.: Stability of almost commutative inverse systems of compacta. Topology of Appl. 31 (1989), 285-299. MR 0997496
[5] Mardešić S., Watanabe T.: Approximate resolutions of spaces and mappings. Glasnik Mat. 24 (44) (1989), 587-637. MR 1080085
[6] Matijević V., Uglešić N.: A new approach to the theory of approximate resolutions. to appear.
[7] Uglešić N.: Isomorphisms in the category of approximate systems. to appear in Glasnik Mat. MR 1283899
Search
Partner of
