 About 122,000 results  books.google.com A topological space is called acompact if it is the union of countably many
compact sets, while a space is called Lindelof if every open cover has a
countable subcover. Clearly every compact space is acompact and every a
compact space ... 

 books.google.com 5.3 Countable Compactness and Sequential Compactness DEFINITION 5.8. A
set A is said to be countably compact if every infinite subset of A has a limit point
in A. Our next theorem shows that a compact set must always be countably ... 

 books.google.com Precompact Sets A set of a topological space is called a precompact set (
countable precompact set) or a relative compact set (a relativecountable
compact set) if its closure is a compact set (a countable compact set). A
topological space is ... 

 books.google.com ... 282Xq, 352Xk, 376Ym countable (set) 111F, 114G, 115G, §1A1, 226Yc, 4A1P,
561A ideal of countable sets 556Xb; see ... 362Ye countably closed forcing 556R
, 556Xb, 5A3Q countably compact class of sets 413L, 413M, 4130, 413R, 413S, ... 

 books.google.com We say that a subset K C U is countably compact if every countable open
covering of K has a finite subcovering. We say that K is relatively countably
compact if K is countably compact. It is clear that a compact set is countably
compact, and that ... 

 books.google.com (2) Let X be a separable locally compact metrizable space with compatible metric
d. It suffices to show that every closed set is a Baire set. Now Lemma 2.76 implies
that X is a countable union of compact sets. Therefore each closed set is ... 

 books.google.com Definitions A topological space X is called countably compact provided that for
every countable open cover U of X ... but not directly related to sequential
compactness, is ωboundedness (every countable set is contained in a compact
set). 

 books.google.com If the family is finite, the cover is called a finite cover; if it is countable or
uncountable, the cover is accordingly called countable ... An analogous
argument proves that (0, l) is not a sequentially compact set in R. Definition—
Countably Compact ... 

 books.google.com The set R of real numbers is not compact, since R is contained in the union of all
open intervals of unit length, but R is not contained in any finite union of such
intervals (see HEINE — HeineBorcl theorem). A countably compact space is a ... 

 books.google.com (ii) ⇒ (i): If T is a quasiSuslin map, each set T(α) is compact. (i) ⇒ (iii) is clear. (iii)
⇒ (iv): Every Lindelöf space is realcompact and thus homeomorphic to a closed
subspace of a product of the real lines. (iv) ⇒ (v): Every relatively countably ... 

 