In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the -closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if is a functionally Hausdorff space, then .
In this paper we prove two fixed point theorems for generalized contractions with constants in complete metric space, which are generalizations of very recent results of Kikkawa and Suzuki.
We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansive mappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finite-dimensional Euclidean spaces.
We prove that (A) if a countably compact space is the union of countably many subspaces then it is compact; (B) if a compact space is the union of fewer than = left-separated subspaces then it is scattered. Both (A) and (B) improve results of Tkačenko from 1979; (A) also answers a question that was raised by Arhangel’skiǐ and improves a result of Gruenhage.