Neighborhood spaces.
Neighborhood spaces and convergence
Neighborhoods of compacta in euclidean space
Neighborhoods of the identity of the free abelian topological groups
Několik příkladů topologických prostorů nesplňujících axiom
Nets and compactness
Network character and tightness of the compact-open topology
For Tychonoff and an infinite cardinal, let the minimum number of cozero-sets of the Čech-Stone compactification which intersect to (generalizing -defect), and let . Give the compact-open topology. It is shown that , where: is tightness; is the network character; is the Lindel"of number. For example, it follows that, for Čech-complete, . The (apparently new) cardinal functions and are compared with several others.
New algebras of functions on topological groups arising from G-spaces
For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urysohn space of diameter 1, we show that SUC(G) is trivial. We introduce the notion of fixed point on a class...
New approach for closure spaces by relations.
New Characterizations and Properties of Almost-open and Almost-closed Functions
New characterizations of regular open sets, semi-regular sets, and extremally disconnectedness
New characterizations of T0-spaces.
New existence of equilibria via connectedness.
New fixed point theorems for mappings satisfying a generalized weakly contractive condition with weaker control functions
The purpose of this paper is to derive new common fixed point theorems for a pair of mappings satisfying a more general weakly contractive condition with weaker control functions in a complete metric space. Applications to new fixed point results with conditions of integral type are also given. We furnish an example to demonstrate that these results improve the previously existing ones.
New metrics for weak convergence of distribution functions.
Sibley and Sempi have constructed metrics on the space of probability distribution functions with the property that weak convergence of a sequence is equivalent to metric convergence. Sibley's work is a modification of Levy's metric, but Sempi's construction is of a different sort. Here we construct a family of metrics having the same convergence properties as Sibley's and Sempi's but which does not appear to be related to theirs in any simple way. Some instances are brought out in which the metrics...
New proofs of classical insertion theorems
We provide new proofs for the classical insertion theorems of Dowker and Michael. The proofs are geometric in nature and highlight the connection with the preservation of normality in products. Both proofs follow directly from the Katětov-Tong insertion theorem and we also discuss a proof of this.
New Proofs that Weak Mixing is Generic.
New properties of the concentric circle space and its applications to cardinal inequalities
It is well-known that the concentric circle space has no -diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of -diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.
New regions of stability in input optimization
using point-to-set mappings we identify two new regions of stability in input optimization. Then we extend various results from the literature on optimality conditions, continuity of Lagrange multipliers, and the marginal value formula over the new and some old regions of stability.
New results in uniform topology