Sentence examples for be a compact space from inspiring English sources

Let be a compact space, a subalgebra of such that.

Hence, let ((X,d)) be a compact space.

Let X be a compact space and Y, Z be arbitrary spaces.

Let B be a compact space such that (dim B=0).

Let X be a compact space and B be a closed subset of X. Assume that (rcolon Xto B) is a continuous mapping and (varphiin A(B,B)).

Lemma 4.3 Let Y be a compact space, let { F 0, F 1, …, F n } be a family of closed subsets of Y.

If is a compact space, then is u.s.c.s.c

If is a compact space and is closed, then is u.s.c.s.c

Assume that X is a compact space and (varphiin A_{U}(X)).

(ii) If is a compact space and is closed, then is u.s.c.   (iii) If is compact and is an u.s.c.s.c

If Y is compact, then F is closed if and only if it is upper semicontinuous, if X is a compact space and F is a u.s.c.s.c