, AN ILLUSTRATED
INTRODUCTION TO
TOPOLOGY
and
HOMOTOPY
S0LUT10NS MANUAL
FOR PART 1
TOPOLOGY
SASHO KALAJDZIEVSKI
IN COLLABORATION WITH
DEREK KREPSKI DAMJAN
KALAJDZIEVSKI
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
A CHA P MAN & HALL BOOK
,CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2018 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business No
claim to original U.S. Government works
Printed on acid-free paper
International Standard Book Number-13: 978-1-138-55346-0 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable
data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their
use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write
and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any
electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any
information storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or
contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978 -750-8400. CCC is a not-for-profit
organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by
the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and
explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
, PREFACE AND ACKNOWLEDGEMENT
This solution manual accompanies the first part of the book An Illustrated Introduction to
Topology and Homotopy by the same author. Except for a small number of exercises in the
first few sections, we provide solutions of the (228) odd-numbered problems appearing in
the first part of the book (Topology). The primary targets of this manual are the students
of topology. This set is not disjoint from the set of instructors of topology courses, who may
also find this manual useful as a source of examples, exam problems, etc.
The help of the two collaborators was invaluable to me. However, all typos and errors are
mine. Comments related to the book or to the solution manual will be appreciated; please
email to . The web page for the book(s) is
http://home.cc.umanitoba.ca/~sasho/sk/topology_homotopy.html; corrections are posted
there.
I am thankful to Mladen Despic for his help. SK
INTRODUCTION TO
TOPOLOGY
and
HOMOTOPY
S0LUT10NS MANUAL
FOR PART 1
TOPOLOGY
SASHO KALAJDZIEVSKI
IN COLLABORATION WITH
DEREK KREPSKI DAMJAN
KALAJDZIEVSKI
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
A CHA P MAN & HALL BOOK
,CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2018 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business No
claim to original U.S. Government works
Printed on acid-free paper
International Standard Book Number-13: 978-1-138-55346-0 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable
data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their
use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write
and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any
electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any
information storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or
contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978 -750-8400. CCC is a not-for-profit
organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by
the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and
explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
, PREFACE AND ACKNOWLEDGEMENT
This solution manual accompanies the first part of the book An Illustrated Introduction to
Topology and Homotopy by the same author. Except for a small number of exercises in the
first few sections, we provide solutions of the (228) odd-numbered problems appearing in
the first part of the book (Topology). The primary targets of this manual are the students
of topology. This set is not disjoint from the set of instructors of topology courses, who may
also find this manual useful as a source of examples, exam problems, etc.
The help of the two collaborators was invaluable to me. However, all typos and errors are
mine. Comments related to the book or to the solution manual will be appreciated; please
email to . The web page for the book(s) is
http://home.cc.umanitoba.ca/~sasho/sk/topology_homotopy.html; corrections are posted
there.
I am thankful to Mladen Despic for his help. SK
