Guoliang Wang is a full professor in the School of Mathematics and Statistics at Beijing Institute of Technology (BIT). He received his B.A. from the School of Mathematical Sciences at Peking University in 2005, and PhD from the Center for Combinatorics (CFC) at Nankai University under the supervision of William Y C Chen in 2010. After that he was a postdoc at Beijing International Center for Mathematical Research (BICMR) and the University of Haifa for two years respectively. Then he was a visiting associate professor at MIT in the 2018–2019 academic year. Professor Wang is the author of more than 30 research papers in algebraic combinatorics. One of his works in topological graph theory was awarded the unique First Prize for Excellent Papers of Youths by the combinatorics sub-society in the Operations Research Society of China.

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• Preface; Introduction; Topological Spaces; Continuous Maps and Homeomorphisms; Connectedness; Separation Axioms and Quotient Axioms; Compactness; Product Spaces and Quotient Spaces; Appendix: Some Elementary Inequalities;

Guoliang Wang is a full professor in the School of Mathematics and Statistics at Beijing Institute of Technology (BIT). He received his B.A. from the School of Mathematical Sciences at Peking University in 2005, and PhD from the Center for Combinatorics (CFC) at Nankai University under the supervision of William Y C Chen in 2010. After that he was a postdoc at Beijing International Center for Mathematical Research (BICMR) and the University of Haifa for two years respectively. Then he was a visiting associate professor at MIT in the 2018–2019 academic year. Professor Wang is the author of more than 30 research papers in algebraic combinatorics. One of his works in topological graph theory was awarded the unique First Prize for Excellent Papers of Youths by the combinatorics sub-society in the Operations Research Society of China.

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• Preface; Introduction; Topological Spaces; Continuous Maps and Homeomorphisms; Connectedness; Separation Axioms and Quotient Axioms; Compactness; Product Spaces and Quotient Spaces; Appendix: Some Elementary Inequalities;

Guoliang Wang is a full professor in the School of Mathematics and Statistics at Beijing Institute of Technology (BIT). He received his B.A. from the School of Mathematical Sciences at Peking University in 2005, and PhD from the Center for Combinatorics (CFC) at Nankai University under the supervision of William Y C Chen in 2010. After that he was a postdoc at Beijing International Center for Mathematical Research (BICMR) and the University of Haifa for two years respectively. Then he was a visiting associate professor at MIT in the 2018–2019 academic year. Professor Wang is the author of more than 30 research papers in algebraic combinatorics. One of his works in topological graph theory was awarded the unique First Prize for Excellent Papers of Youths by the combinatorics sub-society in the Operations Research Society of China.

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• Preface; Introduction; Topological Spaces; Continuous Maps and Homeomorphisms; Connectedness; Separation Axioms and Quotient Axioms; Compactness; Product Spaces and Quotient Spaces; Appendix: Some Elementary Inequalities;