A formal analogy between proximity and finite dimensionality
A formal connection between projectiveness for compact and not necessarily compact completely regular spaces
A formula for calculation of metric dimension of converging sequences
Converging sequences in metric space have Hausdorff dimension zero, but their metric dimension (limit capacity, entropy dimension, box-counting dimension, Hausdorff dimension, Kolmogorov dimension, Minkowski dimension, Bouligand dimension, respectively) can be positive. Dimensions of such sequences are calculated using a different approach for each type. In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived....
A function space C(K) not weakly homeomorphic to C(K)×C(K)
A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ
We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions onto × ℝcp(X)cp(X). One of these examples is compact. This answers some questions of Arkhangel’skiĭ.
A function space C(X) which is weakly Lindelöf but not weakly compactly generated
A function which preserves connected spaces
A Function with Countably Many Ergodic Equilibrium States.
A functional representation of the hyperspace monad
A functional representation of the hyperspace monad, based on the semilattice structure of function space, is constructed.
A Fundamental fixed point Theorem Revisited
A further discussion on Galambos problem.
A Further Extension of Maps With Non-unique Fixed Points
A further generalization of Ky Fan's maximal inequality and its applications
A fuzzy modification of the category of linearly ordered spaces
A fuzzy version of Tarski's fixpoint theorem
A fuzzy version of Tarski’s fixpoint Theorem for fuzzy monotone maps on nonempty fuzzy compete lattice is given.
A -KKM type theorem and its applications to minimax inequalities on -convex spaces.
A Galois connection between distance functions and inequality relations
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set and inequality relations on . Moreover, we also investigate a relationship between the functions of and .
A game and its relation to netweight and D-spaces
We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.
A gauge approach to an ordinal index of Baire one functions
We develop a calculus for the oscillation index of Baire one functions using gauges analogous to the modulus of continuity.
A gauge theory for the Kadomtsev-Petviashvili system