On extended frames
Some aspects of extended frames are studied, namely, the behaviour of ideals, covers, admissible systems of covers and uniformities.
On extensions of uniformly continuous Banach-space-valued mappings
On finest unitary extensions of topological monoids
We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative case, an abstract monoid containing the initial one.
On Generating Quasi Uniformities.
On half-completion and bicompletion of quasi-metric spaces
We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space is quasi-metric if and only if is finite.
On hedgehog-topologically fine uniform spaces
On invariant generalized metrics
On local merotopic character
On metrization of the uniformity of a product of metric spaces
On Nachbin's problem concerning uniformizable ordered spaces
On natural merotopies
On order topology of spaces having uniform linearly ordered bases
On oriented metric spaces
On paracompact uniform spaces
On paracompactness in uniform spaces
On quasi-uniform space valued semi-continuous functions
F. van Gool [Comment. Math. Univ. Carolin. 33 (1992), 505–523] has introduced the concept of lower semicontinuity for functions with values in a quasi-uniform space . This note provides a purely topological view at the basic ideas of van Gool. The lower semicontinuity of van Gool appears to be just the continuity with respect to the topology generated by the quasi-uniformity , so that many of his preparatory results become consequences of standard topological facts. In particular, when the order...
On relatively contractive relations in pairs of generalized uniform spaces.
J. C. Mathews and D. W. Curtis, [4], have introduced some structures which generalize structures of uniform types to the product of two sets, and they obtain a generalized version of Banach's contraction mapping theorem. In this note we prove that these structures are obtained from the usual analogues by means of a particular bijection; hence we do not have a meaningful generalization. For example, this bijection provides, from a result by A. S. Davies, [1], an analogue of Banach's well-known contraction...
On semi-uniformities
On simple recognizing of bounded sets
We characterize those uniform spaces and commutative topological groups the bounded subsets of which can be recognized by using only one uniformly continuous pseudometric.
On some combinatorial problems in uniform spaces