A generalization of the theorem of Mauldin
A generalization of Tychonoff's theorem
A generalization of -sets and -sets by means of operators associated with a topology and associated functions.
A generalized Amman's fixed point theorem and its application to Nash equlibrium.
A generalized continuity and product spaces
A generalized version of the Gale-Nikaido-Debréu theorem
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 generic theorem in cardinal function inequalities
We establish a general technical result, which provides an algorithm to prove cardinal inequalities and relative versions of cardinal inequalities.
A generic theorem in the theory of cardinal invariants of topological spaces
Relative versions of many important theorems on cardinal invariants of topological spaces are formulated and proved on the basis of a general technical result, which provides an algorithm for such proofs. New relative cardinal invariants are defined, and open problems are discussed.
A Geometric Approach to the Bohr Compactification of Cones.
A geometric proof of the Perron-Frobenius theorem.
We obtain an elementary geometrical proof of the classical Perron-Frobenius theorem for non-negative matrices A by using the Brouwer fixed-point theorem and by studying the dynamics of the action of A on convenient subsets of Rn.
A geometric version of the Moore theorem in the case of infinite dimensional Banach spaces.
A Gregus type common fixed point theorem in normed spaces with applications.
A group automorphism is a factor of a direct product of a zero entropy automorphism and a Bernoulli automorphism
A group topology on the free abelian group of cardinality 𝔠 that makes its square countably compact
Under 𝔭 = 𝔠, we prove that it is possible to endow the free abelian group of cardinality 𝔠 with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.
A groupoid formulation of the Baire Category Theorem
We prove that the Baire Category Theorem is equivalent to the following: Let G be a topological groupoid such that the unit space is a complete metric space, and there is a countable cover of G by neighbourhood bisections. If G is effective, then G is topologically principal.
A Hahn-Banach type generalization of the Hyers-Ulam theorem.
A half-commutative IP Roth theorem.
A Hamiltonian property of connected sets in the alternative set theory.
A hedgehog in a product