scholarly journals The intermediate value theorem: preimages of compact sets under uniformly continuous functions

1988 ◽  
Vol 18 (1) ◽  
pp. 25-36
Author(s):  
William H. Julian ◽  
Ray Milnes ◽  
Fred Richman
Keyword(s):  
Continuous Functions ◽  
Compact Sets ◽  
Intermediate Value Theorem ◽  
Intermediate Value ◽  
Uniformly Continuous

scholarly journals The cardinality of the set of left invariant means on topological semigroups

1988 ◽  
Vol 37 (2) ◽  
pp. 247-262 ◽  
Author(s):  
Heneri A.M. Dzinotyiweyi
Keyword(s):  
Large Class ◽  
Topological Semigroup ◽  
Continuous Functions ◽  
Upper Bounds ◽  
Compact Sets ◽  
Lower And Upper Bounds ◽  
Topological Semigroups ◽  
Invariant Means ◽  
Uniformly Continuous

For a very large class of topological semigroups, we establish lower and upper bounds for the cardinality of the set of left invariant means on the space of left uniformly continuous functions. In certain cases we show that such a cardinality is exactly , where b is the smallest cardinality of the covering of the underlying topological semigroup by compact sets.

3. Thinking continuously

2019 ◽  
pp. 48-63
Author(s):  
Richard Earl
Keyword(s):  
Real Variable ◽  
Continuous Functions ◽  
Boundedness Theorem ◽  
Intermediate Value Theorem ◽  
Discontinuous Functions ◽  
Intermediate Value

Many topologists might choose to describe their subject as the study of continuity. There are continuous and discontinuous functions in our everyday routines. ‘Thinking continuously’ aims to provide a more rigorous sense of what continuity entails for real-valued functions of a real variable. It focuses on functions having a single numerical input and a single numerical output. The properties of continuous functions are considered and the boundedness theorem and intermediate value theorem are also explained.

scholarly journals Stirring our way to Sharkovsky's theorem

1997 ◽  
Vol 56 (3) ◽  
pp. 453-458
Author(s):  
Seth Patinkin
Keyword(s):  
Topological Space ◽  
Periodic Point ◽  
Real Line ◽  
Continuous Functions ◽  
Cycle Structure ◽  
Intermediate Value Theorem ◽  
The Real ◽  
Continuous Map ◽  
Sharkovsky's Theorem ◽  
Intermediate Value

The periodic-point or cycle structure of a continuous map of a topological space has been a subject of great interest since A.N. Sharkovsky completely explained the hierarchy of periodic orders of a continuous map f: R → R, where R is the real line. In this paper the topological idea of “stirring” is invoked in an effort to obtain a transparent proof of a generalisation of Sharkovsky's Theorem to continuous functions f: I → I where I is any interval. The stirring approach avoids all graph-theoretical and symbolic abstraction of the problem in favour of a more concrete intermediate-value-theorem-oriented analysis of cycles inside an interval.

ON THREADING CONTINUOUS FUNCTIONS THROUGH COMPACT SETS

1982 ◽  
Vol 8 (2) ◽  
pp. 455
Author(s):  
Akemann ◽  
Bruckner
Keyword(s):  
Continuous Functions ◽  
Compact Sets

scholarly journals Lattices of uniformly continuous functions

2013 ◽  
Vol 160 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Félix Cabello Sánchez ◽  
Javier Cabello Sánchez
Keyword(s):  
Continuous Functions ◽  
Uniformly Continuous

scholarly journals On some properties of the conformable fractional derivative

2020 ◽  
Vol 6 (2) ◽  
pp. 210-217
Author(s):  
Radouane Azennar ◽  
Driss Mentagui
Keyword(s):  
Fractional Derivative ◽  
Conformable Fractional Derivative ◽  
Intermediate Value Theorem ◽  
Definition Of ◽  
Intermediate Value

AbstractIn this paper, we prove that the intermediate value theorem remains true for the conformable fractional derivative and we prove some useful results using the definition of conformable fractional derivative given in R. Khalil, M. Al Horani, A. Yousef, M. Sababhehb [4].

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