### 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)