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A note on approximate limits

Ivan Lončar ; Faculty of Organization and Informatics, University of Zagreb, Varaždin, Croatia

Sažetak

The main theorems of this paper are the following theorems. THEOREM 2.7. Let X={Xn, Pmn, IN} be an approximate sequence of non - empty Čech-complete paracompact spaces Xn such that each Pnm(Xm) is dense in Xn, then limX is non-empty and Čech-complete. Moreover, Pn(limX) is dense in Xn for each n∈IN . THEOREM 2.11. Let X={Xn, Pmn, IN} be an approximate inverse sequence of absolute Gδ - space. Then there exist: a) a cofinal subset M = {ni : i∈IN} of IN, b) a usual inverse sequence Y = {Yi , qij , M} such that Yi = Xni and qij = Pii+1 Pi+1j+2 ... pj-1j for each i,j∈IN, c) a homeomorphism H : limX→limY.

Ključne riječi

Approximate inverse system and limit

Hrčak ID:

79143

URI

https://hrcak.srce.hr/79143

Datum izdavanja:

12.12.1995.

Posjeta: 1.016 *