Some articles on filter base:
... X is a Hausdorff space if and only if every filter base on X has at most one limit ... X is compact if and only if every filter base on X clusters ... X is compact if and only if every filter base on X is a subset of a convergent filter base ...
... Take a topological space X and a filter base B in that space ... The set of all cluster points for that filter base is given by where is the closure of ... The limit superior of the filter base B is defined as when that supremum exists ...
Famous quotes containing the word base:
“What if it tempt you toward the flood, my lord,
Or to the dreadful summit of the cliff
That beetles oer his base into the sea,
And there assume some other horrible form
Which might deprive your sovereignty of reason,
And draw you into madness?”
—William Shakespeare (15641616)