## Real Analysis Exchange

- Real Anal. Exchange
- Volume 25, Number 2 (1999), 879-886.

### Monotone and Discrete Limits of Continuous Functions

#### Abstract

In this note we prove that for a quite large class of topological spaces every upper semi-continuous function, which is a discrete limit of continuous functions, it is also a pointwise decreasing discrete limit of continuous functions. This question was motivated by a paper of Zbigniew Grande. He asked that whether it be true for the topology of right hand continuity on the real line. He gave a partial answer showing that under some additional condition imposed on the function the answer is affirmative.

#### Article information

**Source**

Real Anal. Exchange, Volume 25, Number 2 (1999), 879-886.

**Dates**

First available in Project Euclid: 3 January 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.rae/1230995421

**Mathematical Reviews number (MathSciNet)**

MR1778539

**Zentralblatt MATH identifier**

1011.26003

**Subjects**

Primary: 26A03: Foundations: limits and generalizations, elementary topology of the line 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 26A99: None of the above, but in this section

**Keywords**

upper-semi continuous function discrete limit

#### Citation

Prokaj, Vilmos. Monotone and Discrete Limits of Continuous Functions. Real Anal. Exchange 25 (1999), no. 2, 879--886. https://projecteuclid.org/euclid.rae/1230995421