{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hmw8.1 - Math 655 — Homework ﬂ 1 Suppose that X and Y...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math. 655 — Homework # ﬂ 1) Suppose that X and Y are Tg—spaces. Show that X In: F is also T3. (Hint: First reformulate the T3 condition in an analogous way to the way we reformulated T4 in the proof of Uryohn's Lemma.) 2} Let {(Xm Paﬂaea be an uncountable collection of metric spaces, each containing at least two points. Show that n XE is not ﬁrst countable, hence not metrizable. [X is first countable if for each s: E X we can find a countable collection of open sets {Uﬂ}f=l containing 3:, such that any open set containing 3: includes at least one of the sets UH.) 3) Let {[3}, Pangaea be as above. Can you ﬁnd a metric on n XE... such that [a] the projection maps 1—] X“ —} X3 (b) the injection maps Xﬂ —} n XE. are simultaneously continuous? 4) Show that the Cantor ternary set [“11] — [(1/33/54) Ullfgﬂfgl U WHEN) U - - -l l ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online