175 ALMOST NEARLY CONTINUOUS MULTIFUNCTIONS 1
... The class of nearly compact spaces is properly placed between the classes of quasi-H-closed (i. e., almost compact) spaces and the spaces satisfying the finite chain condition, i. e., every space satisfying the finite chain condition is nearly compact and every nearly compact space is almost compact ...
... The class of nearly compact spaces is properly placed between the classes of quasi-H-closed (i. e., almost compact) spaces and the spaces satisfying the finite chain condition, i. e., every space satisfying the finite chain condition is nearly compact and every nearly compact space is almost compact ...
Logical consequence and closure spaces
... consequence is far more important than that of logical truth, both intuitively and technically. ... Where the notion of logical truth gains its importance is as the limiting case of the consequence relation: there are sentences that follow logically from any set of sentences whatsoever. The crucial ...
... consequence is far more important than that of logical truth, both intuitively and technically. ... Where the notion of logical truth gains its importance is as the limiting case of the consequence relation: there are sentences that follow logically from any set of sentences whatsoever. The crucial ...
A note on reordering ordered topological spaces and the existence
... subset of X that has a maximal (minimal) element is closed. Lemma 8. Let X be a extremely continuous ordered space. Then X is normally ordered and every extension of < on X is continuous. Proof. Let ≺ be an extension of <. Let p ∈ X. Then d≺ (p) is <-decreasing and p is <-maximal in d≺ (p). Also, i≺ ...
... subset of X that has a maximal (minimal) element is closed. Lemma 8. Let X be a extremely continuous ordered space. Then X is normally ordered and every extension of < on X is continuous. Proof. Let ≺ be an extension of <. Let p ∈ X. Then d≺ (p) is <-decreasing and p is <-maximal in d≺ (p). Also, i≺ ...
Tychonoff from ultrafilters
... finite intersections of members of F , and then take all supersets of those. This is a filter, as you should check. In our analysis of filters on topological spaces, we will need to consider the pushforward of a filter F along a function f : S → T . We define the pushforward f∗ F to be the family {B ...
... finite intersections of members of F , and then take all supersets of those. This is a filter, as you should check. In our analysis of filters on topological spaces, we will need to consider the pushforward of a filter F along a function f : S → T . We define the pushforward f∗ F to be the family {B ...