Construction of Spaces

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Construction of Spaces

• Comments on Chap. 5 from Sieradski's book
• http//cis.k.hosei.ac.jp/yukita/

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The choice of topology influences the continuity.
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1.1 Topological Subspace Construction
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Proof of (a)
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Proof of (b)
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Transitivity
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Key feature
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Restriction
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Embedding
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Distinguishing Spaces
embeddable
non-embeddable
Cylinder
Moebius strip
Sphere
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Topological Invariants
non-embeddable
embeddable
Wire handcuff
Wire eight
the cross
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Identification Topology(Dual to the subspace
topology)
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1.5 Identification Space Construction
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Proof of (a)
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Proof of (b)
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Identification Topology
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Ex 4.
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1.6 Theorem A continuous surjection pX?Y that
is either open or closed is an identification map.
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Ex. 6, 7 Identification Maps
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1.7 Transitivity
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1.8 Key Feature
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1.9 Transgression Theorem
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1.10 Corollary
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Quotient Modulo A Subspace
U
X
U
X/A
V
A
V
A