The main purpose of this paper is to prove that if <mml:math alttext="$\mathbf{X} = \{X_a,p_{ab},A\}$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="bold">X</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math> is a usual <mml:math alttext="$\aleph_1$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>&#x2135;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>-directed inverse system
of continuous images of arcs with monotone bonding mappings, then
<mml:math alttext="$X = \lim \mathbf{X}$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mo>lim</mml:mo><mml:mi mathvariant="bold">X</mml:mi></mml:math> is a continuous image of an arc
(Theorem 2.4). Some applications of this statement are also 
given.

<mml:math alttext="$\aleph_1$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>ℵ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>-directed inverse systems of continuous images of arcs


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International Journal of Mathematics and Mathematical Sciences

ℵ1-directed inverse systems of continuous images of arcs

Abstract

Copyright