Uniformly Continuous Sets in Metric Spaces

1960 ◽  
Vol 67 (2) ◽  
pp. 153 ◽  
Author(s):  
Norman Levine ◽  
William G. Saunders
Keyword(s):  
Metric Spaces ◽  
Uniformly Continuous

Uniformly Continuous Sets in Metric Spaces

1960 ◽  
Vol 67 (2) ◽  
pp. 153-156 ◽  
Author(s):  
Norman Levine ◽  
William G. Saunders
Keyword(s):  
Metric Spaces ◽  
Uniformly Continuous

Real-valued models with metric equality and uniformly continuous predicates

1982 ◽  
Vol 47 (4) ◽  
pp. 772-792 ◽  
Author(s):  
Michael Katz
Keyword(s):  
Metric Spaces ◽  
Uniform Continuity ◽  
The Other ◽  
Inference Rules ◽  
Finite Sets ◽  
Uniformly Continuous

AbstractTwo real-valued deduction schemes are introduced, which agree on ⊢ ⊿ but not on Γ ⊢ ⊿, where Γ and ⊢ are finite sets of formulae. Using the first scheme we axiomatize real-valued equality so that it induces metrics on the domains of appropriate structures. We use the second scheme to reduce substitutivity of equals to uniform continuity, with respect to the metric equality, of interpretations of predicates in structures. This continuity extends from predicates to arbitrary formulae and the appropriate models have completions resembling analytic completions of metric spaces. We provide inference rules for the two deductions and discuss definability of each of them by means of the other.

scholarly journals A note on uniform entropy for maps having topological specification property

2016 ◽  
Vol 17 (2) ◽  
pp. 123 ◽  
Author(s):  
Sejal Shah ◽  
Ruchi Das ◽  
Tarun Das
Keyword(s):  
Metric Spaces ◽  
Uniform Space ◽  
Compact Metric Spaces ◽  
Specification Property ◽  
Uniformly Continuous

We prove that if a uniformly continuous self-map $f$ of a uniform space has topological specification property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having specification property. An example is also provided to justify that the converse is not true.<br /><br />

scholarly journals Slowly oscillating continuity in abstract metric spaces

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 925-930 ◽  
Author(s):  
Hüseyin Çakallı ◽  
Ayșe Sӧnmez
Keyword(s):  
Vector Space ◽  
Compact Subset ◽  
Topological Vector Space ◽  
Metric Space ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Uniformly Continuous ◽  
Cone Metric

In this paper, we investigate slowly oscillating continuity in cone metric spaces. It turns out that the set of slowly oscillating continuous functions is equal to the set of uniformly continuous functions on a slowly oscillating compact subset of a topological vector space valued cone metric space.

Hausdorff Distance and a Compactness Criterion for Continuous Functions

1986 ◽  
Vol 29 (4) ◽  
pp. 463-468 ◽  
Author(s):  
Gerald Beer
Keyword(s):  
Uniform Convergence ◽  
Hausdorff Distance ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Compactness Criterion ◽  
Uniformly Continuous

AbstractLet 〈X, dx〉 and 〈Y, dY〉 be metric spaces and let hp denote Hausdorff distance in X x Y induced by the metric p on X x Y given by p[(x1, y1), (x2, y2)] = max ﹛dx(x1, x2),dY(y1, y2)﹜- Using the fact that hp when restricted to the uniformly continuous functions from X to Y induces the topology of uniform convergence, we exhibit a natural compactness criterion for C(X, Y) when X is compact and Y is complete.

scholarly journals Topological entropy and periodic points of a factor of a subshift of finite type

1986 ◽  
Vol 104 ◽  
pp. 117-127 ◽  
Author(s):  
Takashi Shimomura
Keyword(s):  
Finite Type ◽  
Topological Entropy ◽  
Compact Space ◽  
Metric Spaces ◽  
Periodic Points ◽  
Subshift Of Finite Type ◽  
Continuous Map ◽  
Continuous Maps ◽  
Definition Of ◽  
Uniformly Continuous

Let X be a compact space and f be a continuous map from X into itself. The topological entropy of f, h(f), was defined by Adler, Konheim and McAndrew [1]. After that Bowen [4] defined the topological entropy for uniformly continuous maps of metric spaces, and proved that the two entropies coincide when the spaces are compact. The definition of Bowen is useful in calculating entropy of continuous maps.

Sign in / Sign up

Export Citation Format

Share Document