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Ordinal subspaces of topological spaces

✍ Scribed by John Warren Baker

Publisher: Elsevier Science
Year: 1973
Weight: 871 KB
Volume: 3
Category: Article
ISSN: 0016-660X
DOI: 10.1016/0016-660x(73)90034-2

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✦ Synopsis

Let X denote a compact &spemd space with characteristic (~,n). .ks is we&known, the space I?(cY) consisting of the ordinals not excse&ng Q &h the htefvaf top(&)gy has ch;arwteristiz r&n) if and only if &a, < cy < (? l (n f-1). It seems natural to regard the xdir : spaces as "minimal"' dispersed spaces and to co n,kxture that X contains a ?;ubspam Y homecmm~phil: to I'(d -nh It is shun by example that this is ma rht~ casz. We show that if X is onky regular, coun &ably compact, and has characteristic (A,rz) with A <: ga, then it contains 8 subqxze homeomorphic to I'(c3W. However, if X is O-dimensional, firs1 uountable, and has charac%istic (h,ul) with A C SL, we are able to show that it contains a subspace honreomorphic to r(& en). A negat ive a.nswer to a question raised by Senadeni is aho provided.

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