Some articles on open, locally finite open, locally finite, finite:
... space is paracompact if and only if it every open cover admits a subordinate partition of unity ... Lemma 1 If is a locally finite open cover, then there exists open sets for each, such that each and is a locally finite refinement ... Lemma 2 If is a locally finite open cover, then there are continuous functions such that and such that is a continuous function which is always non-zero and finite ...
Famous quotes containing the words open, locally and/or finite:
“GOETHE, raised o’er joy and strife,
Drew the firm lines of Fate and Life,
And brought Olympian wisdom down
To court and mar, to gown and town,
Stooping, his finger wrote in clay
The open secret of to-day.”
—Ralph Waldo Emerson (1803–1882)
“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”
—Clifford Geertz (b. 1926)
“God is a being of transcendent and unlimited perfections: his nature therefore is incomprehensible to finite spirits.”
—George Berkeley (1685–1753)