A formal analogy between proximity and finite dimensionality
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 which preserves connected spaces
A further generalization of Ky Fan's maximal inequality and its applications
A -KKM type theorem and its applications to minimax inequalities on -convex spaces.
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 general coincidence theory for set-valued maps.
A general "in between theorem".
A generalization of a theorem of Polak
A generalization of boundedly compact metric spaces
A metric space is called a space provided each continuous function on into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that spaces play relative to the compact metric spaces.
A generalization of cohomotopy groups
A generalization of normal spaces
A new class of spaces which contains the class of all normal spaces is defined and its characterization and properties are discussed.
A Generalization of the Strict Topology.
A generalization of the theorem of Mauldin
A generalized Amman's fixed point theorem and its application to Nash equlibrium.
A generalized continuity and product spaces
A generating family for the Freudenthal compactification of a class of rimcompact spaces
For X a Tikhonov space, let F(X) be the algebra of all real-valued continuous functions on X that assume only finitely many values outside some compact subset. We show that F(X) generates a compactification γX of X if and only if X has a base of open sets whose boundaries have compact neighborhoods, and we note that if this happens then γX is the Freudenthal compactification of X. For X Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of and the...
A Hahn-Banach type generalization of the Hyers-Ulam theorem.
A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an N-compact space of positive dimension